I, a US citizen, need to apply for unemployment. Can this negatively affect my husband's conditional greencard status/future citizenship eligibility?

Unemployment is not the same as a means tested benefit. You already earned the money by contributing to the fund during the time that you were employed. It should not negatively affect your husband's application although you will still need to demonstrate that he is able to be supported by either you or your cosponsor. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.