That depends on whether the H1 visa holder, your spouse, is still in good standing vis a vis the H1 visa he or she holds.
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I agree with my colleague that it depends on on the status of your spouse's visa. I also think it's important to make sure that you never do anything to endanger your status, so I would check with an immigration attorney. Take all the paperwork related to this and your spouse's visa and explain what you'd like to do.
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Is the H-1 administrative process pending at a US Consul? If so, I doubt that they'll give you an H-4.
Talk to the lawyer(s) involved (your company's for sure ... and possibly your husband's company's immigration lawyer).
Whatever you do do NOT talk to non-attorneys in HR.
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