I don't know what the usual in your state is, but in my divorce I had to pay the premiums on my ex's life insurance (to cover my alimony if he died). I'm not sure I would have felt comfortable with him paying it, because if he let it lapse, I would have been SOL. If your ex has to go out and get new life insurance right now he might not qualify (thinking they may see elevated liver enzymes from his drinking). If he can't get ife insurance at all, this is a situation where getting a lump sum might be preferable, even though the calculations used to estimate that lump sum amount do not usually favor you. (They use unrealistically high estimates of how much that money will grow invested for the future, and unrealistically short life expectancies I believe).
As for Cobra - first of all, your H should be required to keep you on his insurance until the divorce is final. Many workplaces won't let the employee keep the ex-spouse on their insurance after they're divorced. You do get to COBRA the insurance for 36 months after the divorce (rather than the usual 18 months). It can be expensive but in my case, I made too much money to get an ACA subsidy, and while the COBRA was as expensive as the individual policy I got later, the coverage was MUCH better on the COBRA (little deductible, no copays vs what I got later for the same amount was a bronze plan with a $7500 deductible). Your best bet long term is to get a job that gives good health insurance.
