"bank switching" sounds familiar, so I'm pretty sure my memory of 64k is correct then. I can't say I understand what it means, but I remember something of that term at the time.
You group your memory into groups of 16k (could be other sizes, 16k is what I recall but it has been years). Then you have a switch that you can program the switches between groups (also called banks). You can only access one at a time, but you can switch between them very fast. It was possible to get up to 5 MB of memory that way, even though you could only use 64K at a time.