Will a verbal ban from Spain 30+ years ago prevent my husband from taking a cruise out of Barcelona?

For the part about asking for your husbands alerts under the EU transparency regulations, data retention comes in to play in a way that may be beneficial to him. Regulation (EC) No 1987/2006 has this to say...

Alerts for the purpose of refusing entry or stay should not be kept longer in SIS II than the time required to fulfil the purposes for which they were supplied. As a general principle, they should be automatically erased from SIS II after a period of three years. Any decision to keep an alert for a longer period should be based on a comprehensive individual assessment. Member States should review these alerts within this three-year period and keep statistics about the number of alerts the retention period of which has been extended.

Spain joined the Schengen regime in 1991, 4 years after your husband's (alleged) offence. If they entered an alert at that time it would have expired in 1994. Otherwise we have to accept the palpably ridiculous case that they entered an alert in 2015 for an offence that occurred in 1987 and for which there were no judicial proceedings and no indications in his passport. Biometrics did not exist in a real way until the mid 2000's and this further removes the likelihood of a problem.

Note that in all events your husband will still need to qualify as a short-stay visitor.

If he's an EU/EFTA national: He's covered by the freedom of movement and cannot be refused entry into Spain except on serious security-related grounds. In fact, unless travelling from outside the Schengen Area, there won't be any border checks going to Spain.

If he's a visa-free non-EU/EFTA national: Enter the Schengen Area through Portugal or France to be nauseatingly safe. Given that this ban dates back to the pre-Schengen days, it is not something that's going to be recorded in the SIS (common Schengen blacklist); that is, if it's even in the Spanish national blacklist in the first place, which is unlikely given that Schengen bans today last up to 20 years, plus biometrics weren't captured back in those days. Between France/Portugal and Spain, there are no border checks.

If he's a visa national: When applying for a Schengen visa at the Spanish embassy, his fingerprints will be matched against national databases, and you'll know whether the ban's still in force.

Others answerers have suggested applying for a Schengen visa even if you're visa-free, for the purpose of establishing your husband's status. However, it would be worth first consulting the Spanish embassy and asking how they can establish your husband's status. Maybe a visa application isn't a necessary step at all, and I see no reason to assume it is - Schengen embassies are not as "closed" as their UK counterparts.