I had the exact same experience two years ago, also both being in Computer Science in slightly different fields.
In our case our chances were pretty similar as well. However, your sentence ('If you admit me, please also consider admitting my significant other Jane Roe') makes it seem your chances are much higher than your partner's.
If your chances are similar I would mention it in convenient places. For instance when mentioning a project together, talking in person with professors or when a university has a special place to put it (I remember U.Washington had a special field), always remarking that your partner has a similar/better academic level.
If they are not, you can always apply to different tier universities nearby (for example Boston has lots of colleges). Moreover, you should think about how strong the requirement of being in the same university/city is for you. In our case we ended up together in our top choice so there was nothing to reflect upon. However, looking backwards there's two things that I didn't expect that may be useful to think about:
- Having your partner with you makes it much easier to handle day-to-day research's ups-and-downs.
- PhD life has a lot more flexibility than expected: choosing a flexible advisor you could travel and spend multiple days a month together. Specially because in CS you can work from home/abroad.