“Recently, I had a Rav talk to me about how a wife is responsible for her husband’s mitzvah observance.”
I think he meant more mitzvas aseh. I don’t know to which talk you refer, but I presume the point was that the wife gets credit for soliciting her husbands mitzvos such as allowing him to learn in yeshiva, reminding him to daven, etc. That speech is quite common and is used for chizuk for women who might be brought down by the fact that the Torah gives more mitzvos to men. I’ve never heard it having anything to do with issurim; are you sure you didn’t just assume that?
As for the title question, obviously the answer is yes as well as vice versa. People can bring each other down. I don’t believe that was supposed to be the take-away of the talk you heard though.