Our day care charges by the full week (M-F). For families who have children there part time, they pay their weekly rate prorated per the number of days the kids attend.
Because we're full-time at day care, if we have our kids out because they're sick or we're taking a long weekend, it doesn't matter, we pay the full week.
We don't do an in-home daycare, though. We're at a facility who gives us 2 free weeks/year to use at our discretion.
We did have to pay for this Monday, though, despite the center being closed for employee training. That kind of stinks since my husband had to take a day off work as well.