Hypatia, I wish you the best! Keep us posted on how it goes. I suspect that what the rehab center offers is part and parcel of its family program, rather than marital counseling as people normally understand the latter. At family programs, they address how to deal with the alcoholism issues. So, things like boundaries, enabling, detachment, letting go, live and let live, what impact the alcoholism has had on the family, what to expect from rehab, what to do after rehab (e.g., Al-Anon meetings for you; AA for him), etc. While some of those tools can help the marriage, they are given to family members who participate - whether they be a child, parent, sibling, other relative or spouse of the alcoholic/addict. It's about substance abuse and alcoholism treatment for the A and the A's family, not about the typical marriage counseling issues. Insurance coverage impacts that distinction too.
If, indeed, it turns out to be run-of-the-mill marital counseling I'd happily stand corrected because I would love for that to be offered to couples if it would be effective in active addiction, rehab or early recovery.
Hopefully, mry, your H will get therapy for the abuse issues, and you will be able to get individual counseling. I agree with MadeOfGlass' suggestions to you.