Without having seen any episodes of the programme I am going to make some assumptions:
The characters Mitchell and Cam are both men, possibly a gay couple but also, possibly, not.
Mitchell and Cam are, for some reason, which would have been made clear earlier in the script, taking a baby on the plane
The baby is wearing a pair of white or cream furry earmuffs, either because it was cold in the airport, or to stop the noise on the plane disturbing the baby, or because someone had suggested that ear muffs would help stop the baby's ears popping painfully as the plane ascended. The logic behind the earmuffs would have been made clear earlier in the script.
Based on these assumptions I believe that the comedy dialogue is based on a series of crafted misunderstandings:
The woman who says "Look at the baby with the cream puffs" is talking about the earmuffs.
Mitchell, who is probably embarrassed at being one of two men with a baby, hears this, thinks that the woman is using "cream puffs" as derogatory slang for gay men and answers defensively.
Cam points out that the baby is wearing furry earmuffs which could be described as being cream puffs but which also look a bit like headphones. They won't actually be headphones as headphones would be inappropriate for a baby.
To cover his embarrassment at Mitchell's outburst Cam makes a joke offering to pay for similar furry headphones for all the passengers. No one is going to be able to take him up on this because the airline will only have the standard, free disposable ear buds available anyway.
Out of context this just sounds silly, and even in context, doesn't sound like the greatest ever piece of TV situation comedy but it does fit many of the conventions of that genre.
"Cream puffs" probably isn't slang for gay men but "puff" is somewhat outdated offensive British slang for a gay man. Perhaps that is the supposed reason for Mitchell's misunderstanding of the woman's words.
If Mitchell and Cam are straight then that might add to the comedy in the minds of the programme makers.
As I said I've not seen the programme, I've made a reconstruction of the scenario from the dialogue based on years of enjoying some TV comedies and enduring others but I'm sufficiently confident of my interpretation to post this unsupported answer.
