Since your husband is outside the US, he must submit the I-601 after a finding of inadmissibility has been made by the Consul due to previous unlawful presence. Note that if your husband was removed only one time, he will also have to file an I-212, Application for Admission after Deportation or Removal. If he had more than one prior removal he may not be eligible.
You do need the finding of inadmissibility before you can file the I-601. However you can prepare the paperwork needed for the I-601 waiver. My best advice is to consult an experienced immigration attorney.
Alexus P. Sham email@example.com (917) 498-9009. The above information is only general in nature and does not constitute legal advice. It does not create an attorney-client relationship.
I agree with my colleagues.
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At his interview, they will give him a blue notice stating the reasons why he is inadmissible. You need to include that blue notice with the waiver application. Note that, because he was removed he will also need an I-212 as well as the I-601 for unlawful presence. You might want to consult with an attorney regarding his history to determine if there are other grounds of inadmissibility you'll need to respond to.
This reply is intended only as general information and does not constitute legal advice in any particular case. This reply does not create an attorney/client relationship.