You may be able get it only if he accumulated this debt before your marriage. However, your refund may have been different should you filed separately.
I hope my answer is helpful.
My answer is just my thought about your question, and not legal advice because you and I do not have an attorney-client relationship, which may begin only if we both sign a retainer agreement. Other lawyers may analyse your situation differently. Also, the answer may be different in your state. Be aware that I may not be licensed in your state. I am only licensed in Washington and Idaho. Be aware that my areas of practice may not cover your question. I practice Debt Settlement, Business, Asset Protection, Tax Reduction, Contracts, Real Estate Transactions, IRS, 501(c)3, State Departments: Labor and Industries, Employment Security, Revenue, Licensing.
As a general rule, you would be liable for the taxes owed on a joint tax return. However, you may qualify for Innocent Spouse Relief based on equitable relief to get back all of part of your refund. I enclosed links to IRS Pub 971 and Topic 205 on innocent spouse relief.
I would recommend that you meet with a tax practitioner (attorney, CPA, or enrolled agent) experienced in resolving client's problems with the IRS.
You may also want to consult with a family law attorney about what your rights to get reimbursed from your ex you may have and the procedure for getting seeking reimbursement.
I am licensed to practice law only in the state of California. The answer provided above is for general information only, is not intended and should not be taken as specific legal advice and does not create an attorney client relationship with the party making the inquiry. The best way to contact me is by email at email@example.com.