You need to become a naturalized U.S. Citizen in order to petition for what is called an "immediate relative" Form I-130 petition. If your husband has a bachelors degree and appropriate job offer, then he should consider a profesional H1-b visa.
Otherwise, your spouse must wait years to lawfully remain to the U.S. Unfortunately, you may be stuck reading the Visa Bulletin for years, where you file for him as a permanent resident.
How long have you been a permanent resident? Can you apply for citizenship by naturalization, yet? You may have to wait up to five years before you can file. You cannot take long trips outside the U.S. unless you carefully plan. You may also create more trouble where you have a criminal conviction, among other challenges, and file for naturalization. An experienced attorney needs to ask more questions.
This is general information and is not meant to create an attorney-client relationship.
To clarify the answer above, and directly answer your question: You do have the right to file a petition for your husband right now, but your husband will not be able to immigrate for years based on that petition, due to immigrant visa quota backlogs. A petition for spouse of a Lawful Permanent Resident is in the Family-based Second Preferencxe or F2A category, which is backlogged by at least four years or more, depending on nationality. You can check the availability of immigrant visas in each category by looking at the State Department's monthly "Visa Bulletin." Only when the filing date of your petition is earlier than the posted date for the applicable visa category in the current Visa Bulletin would your husband become eligible for an immigrant visa.