I think the best way to go about this is to do it in three steps:
1) Separate, get your own places, get some personal space.
2) Untangle your finances, get to a place where you and your husband are living on separate incomes.
3) Get a divorce. This won't mean you love him any less, but it's a formal committment to breaking those financial and legal bonds that he apparently wants no part of.
Finish these steps before you seek out a new primary committment. These things can be difficult, but it wouldn't be fair to your new man to walk into this situation when it's only half undone. This also gives you time for you to foster your emotional relationship with your husband as the practical things change.
YGirl made a great point about parental rights. There's more: if for some reason (god forbid) you need to adopt, you may not be able to seek out adoption with your new primary if you were still married to your husband. Also, perhaps after you separate finances, your husband happens to go into debt. If you're still married, he would be obliged to report your income as a means to pay off that debt--and if you had any shared accounts with the new primary, his finances would be in jeopardy too.
This all seems very clinical, I know, but it seems like his concerns are mostly these practical issues. If you could both go through these steps, give it some time, and make this separation amicable, I see no reason why the emotional side of things really has to change upfront. It may naturally develop into a secondary emotional connection as you find a new partner, potentially remarry, have children, etc. Just take everything one step at a time, don't jump into things.
Good luck, and be well.