File for divorce, seek spousal maintenance and a share of the marital debts. Consult with an experienced divorce lawyer to assist you. Child support is just for the child's expenses, housing, food and clothing. You may also be entitled to legal fees and an equitable distribution of the marital assets.
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Temporary spousal support is available from your spouse provided the differential in incomes is significant pursuant to a matrimonial action. That can be made for a fixed duration in the judgment. I assume you are living in the mortgaged property. Also, during the litigation, the court could order him to pay part/all of the mortgage if the incomes, again, are disparate and he can afford it. Your attorney will advise you in detail.
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The only way to compel your husband to pay more money would be for you to file for divorce. As part of the divorce lawsuit, the court can order spousal support. If your husband is ordered to pay child and spousal support, he will not be ordered to pay an additional amount for the mortgage since housing is an element of child and spousal support. How much you are granted for spousal support would depend on your respective incomes. However, if your husband makes a lot more money than you do, the amount for child and spousal support may exceed the monthly mortgage payments. Just because the loan is in both names, does not mean that the court will force your husband to pay a percentage of the mortgage. What the court would do instead is have your husband pay child and spousal support. If you are earning less than 2/3 of your husband's income, you will in all likelihood be entitled to spousal support.
You should seek the services and advice of an experienced matrimonial/family law attorney before you reach the point where you are unable to keep up with your mortgage payments.
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A court can order him to contribute to the home expenses even if he is not living there. You should speak with an attorney to discuss your options. Feel free to contact me for a free consultation at 516-488-2255 or contact another qualified attorney on avvo.com
If you have any further questions or would like to speak to me about your case, you can reach me at LanceMeyer@LMeyerLawFirm.com or (516)-488-2255. Legal disclaimer: This is not legal advice and is not intended to create an attorney-client relationship. The post is only an opinion. You should speak to an attorney for further information. I try and answer questions in terms that the readers will understand. The poster is licensed only in NY, CT & NJ. If this post is useful to you, please remember to upvote it.
The short answer is yes he can be made to contribute to the mortgage (but it may not be through additional child support - it may be called spousal support or temporary maintenance (alimony)). If he is on the mortgage, he should have an interest in not seeing it default. Make it clear to him that both of your credit ratings are on the line. If you and he cannot work it out, then you should consider hiring a lawyer. As you can see from the responses, you have several options. Good luck!