To me these notifications suggest that one disk is md0 split into two partitions, and the other is md1 also split into two partitions.
It's the opposite. The physical disks are 'sda' and 'sdb'– the RAID arrays are 'md0' and 'md1'.
Each disk is indeed split into two partitions (sda1, sda2, sdb1, sdb2) and each pair of partitions has a RAID array configured on it. If you run lsblk you'll probably see something like this:
NAME SIZE TYPEsda 466G disk├─sda1 8G part│└─md1 8G raid1└─sda2 458G part└─md0 458G raid1sdb 466G disk├─sdb1 8G part│└─md1 8G raid1└─sdb2 458G part└─md0 458G raid1
So the physical disk /dev/sda has failed, and it was acting as a member of both the md0 and md1 arrays. (Probably a small portion of the space was used for the '/boot' volume and the remainder for the rootfs.)
To find out which disk it is physically, use lsblk -S or lsblk -do name,tran,model,serial,wwn.
Replacing the disk can likely be done live, using mdadm --manage. (I think the exact commands depend on whether you first connect the new disk as 'sdc', or whether you directly replace the old disk and it remains 'sda'...)