It is likely you will file as married. However, if you have been in the country less than 5 years you are most likely filing as Non-resident alien on a form 1040NR. TurboTax does not support that form however you can use Sprintax for assistance with the correct filing/status.
If you have been in country over 5 years and pass the substantial presence test you may be filing as Resident alien. In that case you will file a form 1040 as married filing separately or possibly as head of household in special circumstances. Here is a link with more information.
You will need to obtain an Individual Tax Identification Numbers (ITIN) for your spouse and children. Here is a link with options to secure ITINs.
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