You are not legally liable for child support for a chiild that is not biologically yours (or yours by adoption). However, if future hubby defaults on his payments for any reason, an intercepted tax refund, for example, might not distinguish between how much of the refund is yours versus how much is his, if you file your taxes jointly. Any assets that are jointly owned could be at risk. However, the state usually does not go after assets unless the arrears get pretty high.
Usually, the new partner's income is not directly factored into the support obligation. However, some of his overall living expenses could be less and that could factor into the CS calculations in some states.
If your spouse lost his job, he needs to file for a modification or reduction of his CS obligation ASAP. Child support modifications are seldom retroactive, so the longer he waits, the deeper the hole can get. Since some people find new work very quickly while others need more time, the CS enforcement agency may allow him to make temporailry lower payments until such time as he obtains new work at which point, he would be expected to "catch them up". If he is in a field where finding new work is going to take awhile, he might want to consider a more permanent modification of his CS obligation should this one happen.
As a practical matter, when you are married, you are on the financial ship together. If one of you puts a financial hole into the ship, you both probably will sink. But, you cannot be held directly liable for his obligation.