I agree with the above. I could put my DS down after 15-20 minutes, when he was in a deep sleep, but sooner than that would wake him up.
Yes, some slings you can feed in. Or you could pick her up after she's fed, put her in the sling and go out for a walk/move around indoors (depending on how much motion she needs). She may well drop off then, and you'll have your hands free.
Alternatively, if your bed is set up for safe co-sleeping, you could feed her lying down and leave her to sleep on the bed. Do make sure it is safe if you do this, though.
As seeker says, many babies do like being wrapped. You could try swaddling in a thin sheet.
My DS stopped falling asleep at every feed when he was only 2 weeks old so I'd then rock/jiggle him to sleep. I think that was fairly young, though, to stop falling asleep after every feed.
Congratulations and keep going. Your DH probably doesn't understand enough about babies' development to know what settling methods are likely to work at this stage. I know my DH kept suggesting controlled crying when DS was a month old and unsettled - he simply didn't understand that things like that don't work with tiny babies.