Hi all! Thanks for your comments!
To answer a few questions - I'm in Germany, and in the area I'm in its pretty normal to have a washing slot. I also used to live in Switzerland where we had the same arrangement, so I'm used to it (you DO get used to it).
We both forgot that the card didn't have enough credits on it, hence having to urgently get a new one just before our slot.
It's not laziness with my husband, it's awkwardness. He hates talking to the concierge because the man talks a lot and my husband's German isn't amazing, so he dreads it. But I still think he needs to get a grip because it wasn't worth waking our baby to do (also, just on principle, I know he will just start to let me do everything German-related if I don't insist that he does his bit. The way I see it, his German will only get better if he practises it!).
We don't take "turns" with the laundry card. These were my husband's words, not mine. I thought he was being childish and ridiculous so I wanted to see if other people agreed and show him.
To the people saying put the baby in a sling, my baby HATES slings with a passion. And she is not easy to get back to sleep, which is why I was reluctant to wake her. Parents of reflux babies, you know what I'm talking about!
However, as an update, I did pass her to my husband and she did wake up. We needed a laundry card and he point blank refused to do it.
He's not like this with everything. He pulls his weight in most ways, but things that require German, he doesn't. The reason why I am trying to push the German is that we've been here for two years and he still can't speak it, but he is working from home three times a week and he'll be the one to collect the baby from nursery if the baby is sick, so he needs to get a grip imo and stop avoiding situations where he has to speak German (and he CAN speak it, he just doesn't want to).