Answer:   Yes, GI Bill benefits are transferable.

The Post-9/11 GI Bill allows Servicemembers to transfer all 36 months or some unused portion of their benefits to their spouse or dependent children, or any combination of spouse and child while on active duty.

Family members must be enrolled in the Defense Eligibility Enrollment System (DEERS) and be eligible for benefits at the time of transfer to receive benefits. The Department of Defense (DOD) makes the determination, and once approved, the new beneficiaries may apply to use transferred benefits with VA by printing, completing, and mailing the VA Form 22-1990e to their nearest VA Regional Office. Use of the benefit starts immediately and can be used for up to 15 years after separation from active duty for spouses. Dependents are not subject to the 15 year rule, but may not use the benefit after reaching 26 years of age.

For more information about transferring GI Bill Benefits, please read the VA PDF pamphlet below:
POST-9:11 GI BILL- TRANSFERABILITY