I hope this message finds you well, present circumstances excluded. I am a licensed attorney with over a dozen years of experience handling matters of this nature. It is a pleasure to assist you today.
The answer is yes, you can get him to pay since he is your husband and since he is on the lease. However, unfortunately, the only way to legally make him pay is to file for divorce and have the court issue a temporary order against him for him to pay what he has been contributing towards the lease while the divorce proceedings play out.
In essence, you will file for divorce for abandonment. In a petition, you will ask the court to enter a separation agreement wherein he is ordered to pay your lease as he was doing prior to leaving you.
I wish there was another way here, but unfortunately, that is the legal mechanism to handle this problem. I am so sorry.
Let me know if you have any other questions or comments. Please also rate my answer positively (THREE OR MORE STARS) on the ratings bar on your end.
Thank you and best wishes!