Sorry if this is an obvious question. I earned a MS in psych, went and worked a few years, and I'm thinking I want to go back and finish out the degree, earn a PhD. More than one of my professors at the time I was in school recommended I go on, but for personal reasons it wasn't the right time. I know they'd happily write a letter now, but is that appropriate given they're also program faculty? My current employers are willing to write letters as well (I work in MH) but I know there's usually at least one academic reference, and if I can't use the graduate school ones that's going to be a challenge.
You certainly can and it is often useful in the ways that Michael M. notes. However, there can be a downside in that it effectively reduces the number of useful letters of recommendation by one.
In other words, the people in program who know you already know you. If they are on the admissions committee, then they will (if they support your candidacy) speak up for you. When advocating, it's handy to have ammunition in the form of external evaluations.
Scenario: I am a Professor at University X and I really want AS2045 (who is at X) to continue to the PhD program. I'm also on the admissions committee. When promoting her case to my peers on the committee, I would find it more useful to have 3 outside letters that say she's brilliant ("Prof. A, Prof. B. and Prof. C @ OtherU think she is brilliant, and so do I!") rather than 3 letters, one of which is my own -- making it effectively only 2 that I can use to argue my point.
tl;dr: If the person is on the admissions committee, then ask them for their advice -- would they prefer an external letter from another person or do they think their own letter would suffice.
Note: If they aren't on admissions, then certainly include the internal letter.
I think that would be a great idea: your references are supposed to be advocating for your ability to perform the work of the program, right? Well, who would know better than people running the program?
If one of the program faculty gets asked about you over coffee in the morning, and they say "Oh, AS2045? Yeah, he was in my undergrad classroom, and I think he'd be a great fit for our program, bring in a ton of good grants," then odds are, you're going to do well there.