Since you are not subject to the INA Section 212(e) requirement, you could change your status to H-1B, which could provide you with up to 6 years of work authorization with your employer. But the H-1B category is capped each year, and the number of visas given out are close to being exhausted, so you'd need to act very quickly. Permanent resident status is also a possibility, but your employer would need to test the labor market and file a PERM labor certification application to begin. I think you should consult an experienced and reputable immigration lawyer that could respond quickly on your employer's and your behalf.
Mr. Pollack is spot on. Additionally, I'd talk with your employer immediately about their petitioning for an H-1B for you at the very least. This gives you and your wife some flexibility. If one of you is laid off, the other doesn't have to scramble to become the principal/anchor non-immigrant. As well, the H-1B gives you the dual intent proviso that will permit filing for an EB based green card.