Most states these days stipulate that divorcing spouses split marital assets and marital debts more or less evenly unless they agree to different percentages. Basically, anything acquired during marriage is considered marital, regardless whether one person paid for it or not.
There's a small number of situations otherwise, like infidelity, but the bar for proof is high.
Assuming more of his debt is a good negotiating tactic but you say he's not cooperating.