How to mention that we are applying as a couple?
Different universities will have different rules. At some you will be strictly considered as individuals. At others some accommodation might be made, but only at the margins. You can just state in your cover material that you are seeking positions together for personal reasons.
But it is worth mentioning, so that the admissions committee is aware that you have some constraints. But if you are both marginally qualified, by their rules, it would be more a reason to reject both than to admit both.
But is is unlikely that one would be admitted if unqualified even if the other is highly qualified. Being married is probably better than just being &quot;together&quot;.
Another possibility for you, however, if you are willing to live in a large city, is to make applications to several universities in some city, like NYC or San Francisco. Then it would be feasible to attend different universities, though such places tend to be expensive to live in.
And the application would be for the doctorate. It is unnecessary to mention a masters in such an application. A masters is normally earned &quot;along the way&quot; to the doctorate, sometimes just by asking and sometimes with some fairly minor additional requirement.