Speaking as the wife of a builder:
The customer has paid for a job to be done, it hasn't been done to their personal satisfaction so they are within their rights to complain. The only thing your husband can control is his response to the complaint.
There should be no grout on the surface of the tiles, that's not a job done to a professional standard. There may be a 'haze' after cleaning, but he should be cleaning that off too. It's no good leaving the job before they're dry and he can't see what they're like.
If your husband doesn't have the experience to do the job (in this case work with textured tiles) he shouldn't have quoted. If he doesn't know his limitations then he's unfortunately going to get a reputation for shoddy work, not the good rep he's trying to build.
Giving discounted prices is all very well, but unless it's because it's 'mates rates' and the customer knows that then it isn't relevant - he chose the price, not the customer. If you bought a dress a little cheaper in one shop rather than another would you not complain it had a hole in it because it was 10% cheaper?
He needs to say to the customer that he'll rectify it, and do so.
The only issue here is he's tried unsuccessfully to fix it once - potentially the customer has fears they've hired a cowboy and they're afraid of damage being done to the tiles.
And you really shouldn't be rocking up to his jobs, that's quite weird!