You need to consider mediation, which is a non-compulsory procedure that attempts to fashion a win-win scenario instead of litigation which is almost always a win-lose.
You are correct both are liable on the lease. If you can't work it out, perhaps you can both sublet so that neither benefits to the detriment of the other.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
I agree with Mr. Doland. I would add that neither of you can exclude the other from the premises absent an agreement to that effect.
This answer does not constitue legal advice, nor does it creat an attorney/client relationship. If you are seeking legal advice upon which you intend to rely, you should hire competent cousel familiar with this area of the law in your locale.
I agree with my colleagues' excellent answers. You are both probably liable for the entire rent and cannot exclude the other. Thus, some form of cooperation is essential.
I want to point out some newer leases require mediation before litigation or you cannot recover your attorney's fees if you prevail. This creates a strong incentive to mediate. Thus, you should carefully read your lease.