Can my husband claim injured spouse and our 3 kids if my taxes are offset for student loans?

[AnthonyJ]

Yes.  Your husband is able to file Form 8379 "Injured Spouse" as long as he had income himself.  

Generally, if you are reporting your own income and are filing as Married Filing Jointly, you can file Injured Spouse and it is your choice how many dependents you'll claim and how many will be allocated to your husband.  TurboTax will ask you for that allocation when going through the Injured Spouse interview.

NOTE:   If you file Form 8379 with your original return, it may take 11 weeks to process an e-filed return or 14 weeks if you filed a paper return. 

If you file the Form 8379 by itself after a joint return has been processed, then processing will take about 8 weeks. 

To avoid delays, be sure to follow the Form’s instructions.  Below is the link to the Form 8379 instructions for you.

://www.irs.gov/pub/irs-pdf/i8379.pdf