Military Spouse Career Education Act This bill (1) includes as qualified relicensing costs fees and continuing education courses, and (2) allows the reimbursement of a member of the uniformed services for the qualified relicensing costs of a spouse when such costs are imposed to maintain a license or certification to engage in the same profession that the spouse engaged in while in the state of the original duty station, and are imposed by the state of the new duty station to maintain a license or certification to engage in the same profession. The Department of Defense shall modify its My Career Advancement Account program to ensure that military spouses participating in the program may receive financial assistance for the maintenance (including continuing education courses) of a license, certification, or Associate's degree in any career field or occupation.