Firstly, please don't feel embarrassed. His situation and your situation are miles apart. You're pregnant with your second child, live independently, stand on your own two feet and have a husband.
I would try and confine in your husband, a problem shared is a problem halved.
And just say it to him how you have here, you don't have to support the situation but sadly, it is what it is.
You're probably right that they won't stay together in the long run, sadly people do this daily, jump into relationships and bring kids into the equation before they really even know one another. The added stress of a pregnancy, money, and then a baby break couples like that very easily.
And your parents need to set a deadline: by say March of next year, he needs to be out and in his own place supporting the mother of his child. It's not unfair, he's a grown man, who's about to become a father himself, time to step up and take care of himself and the situation he's found himself in.