I have an AA in Liberal Arts and am one semester away from an AS in Computer Programming and Analysis. I will have to double check the numbers but I will have around 140 credit hours which is similar to the number required for a Bachelor's degree. Is this equivalent somehow to a Bachelor's? In general, do two lesser degrees equal one higher degree (e.g., do two BA degrees equal a MA or two MS degrees equal a PhD)? Is there any number of lesser degrees that would equal a higher degree? Why or why not?
From an educational perspective, community colleges usually do not offer courses beyond a sophomore level. Therefore, the bachelor's degree will probably contain more depth than an associate's degree. For example, an AA in economics will probably stop with intermediate microeconomics, but a BA may include advanced courses in microeconomic theory.
From my experience, in the UK at least. It's irrelevant how many qualifications that you have at any particular level, they never add up to the level above.
For instance, you could have 20 GCSEs, but someone with 1 A Level would still be considered qualified to a higher level than you.
The same goes for degrees, you can't add up Bachelors degrees to make a Masters or Masters degrees to make a PhD.
However, that being said, in Europe we have a system known as the European Credit Transfer Scheme, where you study modules worth a certain number of points (these also have associated levels) and should you change institutions, you can carry over any of these that haven't been assigned to a particular qualification.
Thus, if you studied for two associate degrees and two different institutions but never got awarded them, you might have enough credits to be awarded a bachelors. However, it is doubtful that you would have sufficient credits at the right levels.
Employment: I recommend that you make some appointments with people in your computer programming department for career counseling. If your community college has a person who coordinates Co-op Education, that person would probably be a good starting point.
Of course you can apply for jobs with an Associate's. You won't know for certain how you will fare until you do. (Do take a close look at the requirements for the jobs you are interested in.) But two Associates are not equivalent to one Bachelors. You are missing all or almost all the upper level classes. In addition, some community colleges' courses are not well aligned with those of the state university in the same state. You can find out more about the alignment in your state by asking for a pre-transfer transcript evaluation (note you may do this whether or not you will actually transfer to that school), or by speaking with the person in the state university's computer science department who evaluates transcripts.
Academically: you can't apply for a graduate program without a Bachelor's degree.
Note: Liberal Arts study makes you a good reader, thinker and writer. Your programming classes make you a programmer. The programming classes prepare you for programming (and related) jobs. The liberal arts classes are great for personal growth, but they don't directly strengthen your technical skills.
Take a look at the program of studies in Computer Science in your state university, and you'll see that there's plenty of worthwhile work ahead of you in the second half of your undergraduate studies.
I understand this is Academia.SE, but I wanted to address both areas OP has inquired about.
It all depends on how the job description is written. For example, if the job description clearly states "Bachelors degree in XYZ" then the two Associates degree won't count and you wouldn't be able to truthfully fulfill the requirement. However, if the job description states "Bachelors degree and/or equivalent experience and/or education" then you could argue that you fulfill that requirement. (Having worked in HR, those requirements are very real because employers now recognize that the best person for the job may not have a Bachelors degree.)
In regards to furthering your education, you would never be accepted into a Masters or PhD program without having at a minimum a Bachelors degree. This is because Bachelors degrees often end with a capstone or thesis, which sets the foundation for the research skills needed to complete graduate level courses. Associate degrees don't offer the same rigor.
But at the end of the day, no, two associates degrees do not equate a Bachelors degree. Associates degrees equate to the first two years of a Bachelors degree, so it is missing out on the upper level classes, capstones, theses, etc.
To answer your question are any combination of lower degrees equivalent to a higher degree, the answer is no. As to why it has to do with how the degrees are designed.
Associates degrees are designed to convey technical specialization in a very narrow area. It emphasizes training over education. It tends to emphasize foundational skills in a profession with the goal of mastery. A bachelor's degree, in contrast, tends to emphasize education over training. The first two years tend to provide a broader base of skills, including skills far afield from the profession implied by the major chosen. This allows a person with a bachelor's degree to integrate their skills into other industries. The second two years are about developing expertise within the field along with some increased depth outside of the primary field.
A person with a bachelor's degree has met just enough education to say they have a basic level of expertise in a topic. This contrasts with a master's degree. The goal of the master's degree is to provide sufficient technical expertise in the field so as to be capable of teaching it without supervision. The master's degree emphasizes depth over breadth. The job of the undergraduate degree is breadth. The job of the master's degree is to convey depth. The courses are not designed to add new information, they are to add knowledge from that information. Within the field, it conveys how the world works to the current level of knowledge.
The doctorate exists in two forms, the professional doctorate and the doctor of philosophy. A good example of a professional doctorate is the MD. This differs from a physician's assistant, which is basically a master's degree, in that a PA learns hundreds of algorithms to treat a patient. The MD learns enough to understand why the algorithms the PA uses work and when the algorithm fails, will have learned the underlying biological principles to design a new algorithm to fit the very specific needs of a patient where the general rules are failing them.
The doctorate in philosophy has an opposite goal. The job of a Ph.D. is to figure out what we believe to be true is actually false. It is to research how the world works. The job is to understand the implications of ways of thinking about problems. It's important to remember that if there is something that we believe that is actually false, it is understood in such a way as that it makes perfect sense for it to be true.
In fact, you can't make a mistake by believing you are making a mistake. You have to do it by believing you are not making a mistake. Everything has to make perfect sense. The job of the Ph.D. is to notice when mistakes are happening when they are not supposed to be happening and that are actually systematic mistakes and not just one-off mistakes. Your Ph.D. is awarded after you have completed research that extends the frontiers of knowledge.
The training of doctorate isn't like the master's training. The master's is not like the bachelor's and the bachelor's is unlike the associate's. They don't combine. You should contact a bachelor degree granting institution and see what could transfer into a bachelor's program. You should see how far you are from a BA or a BS degree. It will pay better and will probably not require a mountain of additional work.