@fma2022 , while @Vanessa A reply was generally responding to the question you asked --- can your husband ( a Valid Green Card holder ) file as Married Filing Separate -- is correct but it did not go far enough because it did not offer another choice that your husband has.
As a US person ( Citizen/Green Card ) living in another country along with a child related by blood or adopted, for whom your husband maintains a home and pays more than 1/2 of his/her living expenses , he can claim Head of Household filing status. This offers him a more tax benign situation ( higher standard deduction ) and also allows for child credit etc.
Note we all keep repeating a statement --" with valid Green Card". This is because to keep one's Green Card valid while one is abroad, (a) one must return / touch US soil at least once every 1 year or (b) get permission from INS to stay away for Three Years. In my time I applied before leaving the US shores but it is possible to go to the local US embassy/consulate ( in Shanghai ) and this cleared up-- else when he comes back to USA he will need a new visa ( he would be deemed to have abandoned his permanent residency). I hope you were aware of this and has taken care of this.
In some very specific situations / countries one spouse whom maintains a household and a Non-Resident Alien lives therein, the spouse can be a dependent -only for exemption purposes ( which is currently zero through 2025 ).
Does that clear up all your issues or is there more I can help you with?
Also note that this probably also answers a similar question from Feng ( assume that is your spouse ).
pk
