He can submit a request for extended leave, or potentially a humanitarian re-deployment. However, this is rarely granted in his situation. The circumstances for you at home would have to be very extraordinary and well documented for him to have a chance. Absent the extraordinary nature of the medical concerns they would view his request along the lines of "lots of people have family problems, why is yours different."
No doubt you are concerned about the pregnancy without him present, but you likely have no alternative. Strongly recommend you use the wide e range of services available on base including legal aid, financial aid, parenting classes, ombudsman support, support groups etc.
I am licensed in the Commonwealth of Virginia, answering your query does not create an attorney-client relationship and I AM NOT providing you legal advice. You should speak with an attorney to whom you have provided all the facts, before you take steps that may impact your legal rights--or rights to recovery of damages. I wish you the best of luck with your situation.
I agree with my colleagues in thier answers to your question. It is doubtful that the military will treat your pregnancy as a medical emergency that warrants extended leave.
Based on your location, I am assuming your husband is stationed at Ft. Bliss. I encourage you to contact the Army Community Servcie Center on the base. The following information is from the Ft. Bliss FMWR web-site. (http://www.blissmwr.com/frg/) I would suggest starting there to find out what resources are available to you for assitance with child care, etc.
Army Community Service now has two locations to better serve you: the main post location and a new annex on East Fort Bliss!
If you're out east, save time and gas by visiting the East Bliss annex at Bldg. A-479 Kasserine Rd., located between Saber and Thunderhorse roads. All ACS services are available at this location. Take advantage of full-service programs from Information and Referral, Financial Readiness, Mobilization and Deployment, Relocation Assistance, Exceptional Family Member Program and the lending closet. Limited services are offered by the Employment Readiness Program, Army Family Action Plan, Family Advocacy Program, Army Volunteer Corps, Army Family Team Building and Army Emergency Relief (located in A-478). If utilizing any of these services, call the main post ACS, Bldg. 2494 Ricker Road, determine which office can best serve you.
For more information, call the ACS East Bliss annex at (915) 744-1435 or the main post ACS at (915) 569-4ACS (4227).
I would also suggest contacting your local YMCA to sign up for the free military family membership while your husband is deployed. At many of the YMCA facilities, drop-off babysitting/daycare is offered to the families of deployed service members.
I wish you and your family well during this deployment. I appreciate the sacrifice you are all making for our country.
Disclaimer: Transmission or receipt of information does not constitute an attorney-client relationship.