The VDP can generate two different types of CPU interrupt.
The first, and easiest, is the frame interrupt, which is requested when an entire frame has been generated. This is requested, therefore, at a regular 60Hz in NTSC regions and 50Hz in PAL regions - it's a useful timer to synchronise your game to.
The second, and more complex, is the line interrupt. This interrupt is requested when a user-definable number of scanlines have been displayed. An internal counter is decremented each active line (and one more just after), and when it overflows it resets to the value held in a VDP register and requests the interrupt (so 0 would request an interrupt every line, 1 every other line and so on). For every other line outside the active display area, the counter is reset to the contents of the VDP register.
Both interrupt types can be enabled or disabled by defined bits held in the VDP registers.
(The above should be loosely correct, the below is a little more uncertain).
Once an interrupt is requested, a flag for said interrupt is set. The flag is not reset until the VDP control port is read, so you must read the VDP control port if you expect any further interrupts.
To differentiate between line and frame interrupts you can check the value read from the control port. If the most significant bit is set, a frame interrupt (at least) was requested. Reading the vertical counter port (which returns the current scanline's vertical position) will also let you know where you are.
Something is a little wonky with my vertical counting code, as all lines end up being one too large. For the moment I'm subtracting one before returning the value (and waiting one extra scanline before triggering the frame interrupt) which is a horrible solution, but for the moment it has fixed a number of games that weren't working at all before.
Earthworm Jim, which relies on line interrupts to switch on zoomed sprites to dipslay the status bar at the bottom, now plays. It's missing some graphics on the title screens, though.
For some reason, rebuilding my Z80 emulator (which is in a different project) fixed some other interrupt-related glitches, so I have a sneaking suspicion most of my earlier problems are related to using an out-of-date DLL.
Road Rash highlighted another bug. The VDP can draw doubled sprites - that is, when a particular bit is set it will draw sprites as 8x16 pixels, stacking two consecutive sprite tiles on top of each other. Road Rash uses this mode, but also uses odd sprite indices (odd as opposed to even, not strange). The VDP will only take even indices, so a line of code to clear the least significant bit if using doubled sprites fixed that.
Still no sound, though.