There is no state time limit per se but there is a federal time limit which is 1 year from the final decision of the state appellate court plus the 90 days that could have been used to file in the Supreme Court (assuming a PDR was filed.) The 1 year time limits is tolled by the "proper filing" of a state habeas petition.
He needs a lawyer hired to represent him as, in general, there is only one bite at the habeas apple.
If you are asking about federal habeas corpus, it is really best to have an attorney familiar with that kind of work calculate the filing deadline, because getting it right can be rather tricky and the consequences of getting it wrong are very serious indeed and a habeas petition is not something that can be thrown together at the last minute. Also, the time limit for filing a federal habeas petition has to be taken into account in deciding when to file a state collateral petition, such as a state habeas or post-conviction petition. Federal habeas is an exceptionally complicated area of the law and even most good and experienced criminal defense attorneys do not know much about it.
I agree with the timetable contained in Ms. Hensley's answer. The one-year time limit should be followed so that a habeas petition can be filed in federal court if it is denied by the Court of Criminal Appeals of Texas. If the state habeas if filed after one year from the date the direct appeal concludes, there will be no right to federal habeas review after the state habeas petition is ruled upon.
You husband should also be aware that if the intermediate court of appeals affirms your husband's conviction, he has the right to file a petition for discretionary review (PDR) with the Court of Criminal Appeals of Texas (in Austin) asking that court to review his appeal. The PDR must be filed within 30 days of the court of appeals' opinion, and four of the nine judges must vote to grant review for the case to be heard. While Texas law permits a court-appointed attorney for indigent defendants for the direct appeal to the court of appeals, there is no right to a court-appointed attorney for filing a PDR. Once a decision on the PDR is made, if there is a federal constitutional issue, a petition for a writ of certiorari can be filed in the United States Supreme Court within 90 days of denial of PDR. Just as with the PDR, 4 of the 9 Supreme Court justices must vote to grant review, otherwise certiorari (review) is denied. Once that happens, the one-year habeas timetable will begin.