If my husband is still living in the residence, do I have a legal right to his payroll check to pay bills with?

This question is NOT as simple as you are portraying it to be as you have not stated where the husband's paycheck is. Is it deposited into a joint account? Are YOU cashing it for him and then using it? Does he have a separate account into which it is deposited and you want to utilize that separate account?
Money earned during the marriage is, simplistically enough, marital income, however that does not mean that you legally have the right to utilize it. How you are planning to access the funds matters. Also, what bills need to be paid that husband's check would pay? Do you work? Were you planning to just demand his check so you can pay bills? In whose name are the bills?

There are many questions that are taken into consideration.

The simple answer is that you may continue to pay marital bills from the accounts on which your name is located -- including an account into which his pay may be deposited. You cannot force him to deposit his check however into said account or accounts.

If he is the primary breadwinner and you are engaged in a divorce, you may need to seek temporary orders to provide for expenses that occur during the divorce.

I need to ask first: what is the status of your marriage?  Are you still legally married or do you have a separation agreement in place and he just still resides there?  Or have you filed for divorce?  Of you have filed for divorce has there been any temporary award of support?  And determination as to the bills? These questions matter in giving any guidance here on this question.  In general terms you and your husband are obligated to keep paying your bills while what ever is going on and without an agreement in place.  Money earned during the marriage are marital funds.  But I would strongly suggest you seek legal counsel and let him or her know where you stand given your situation.  Good luck.