Mexico normally does not run a criminal background check at the border or port of entry, and as a US citizen, he should be able to enter and exit back to the US.
That said, authorities may decide to refuse the request to enter the country if the applicant is subject to criminal process or has been convicted of a serious crime as defined by national laws on criminal matters or provisions in international treaties or conventions that the Mexican State is party to, or if the applicant’s background in Mexico or abroad could compromise national or public security, in accordance with Article 43 of the Migration Law.
According to Article 194 of the Federal Code on Criminal Proceedings, serious crimes include all crimes that have a significant, negative effect on the fundamental values of society.
Serious crimes include, among others: manslaughter; terrorism and international terrorism; sabotage; piracy; genocide; prison break; attacks on public thoroughfares; drug-related crimes; corruption of minors; child pornography; exploitation of minors; falsifying and counterfeit of currency; rape; highway robbery; trafficking in minors; trafficking in undocumented persons; aggravated robbery; vehicular theft; extortion; crimes against the environment, committed with intent; forced disappearance of persons; bearing arms reserved for the exclusive use of the Army, Navy or Air Force; smuggling into the country firearms not reserved for the exclusive use of the Army, Navy or Air Force; smuggling and comparable crimes, and; tax fraud and comparable crimes.
Thus, the people who have problems are person with serious criminal offenses on their record and those persons on probation or parole. The fact that your husband was able to enter and exit fine previously in August suggests he shouldn't have a problem this time. However, it certainly wouldn't hurt you to call your local Mexican consulate to verify all of this and policies can and do sometimes change, and this way you'll have the most up to date information.
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