There are 100 different ways to skin this cat, depending on CPU architecture (interrupt nesting & prioritization, software interrupt support, etc.) but let's take a pretty straightforward approach that is relatively simple to understand and free from the race conditions and resource-sharing hazards of a preemptive kernel.
(Disclaimer: my first choice is typically a preemptive real time kernel, many of them can run in extremely resource-constrained systems... SecurityMatt's suggestion is good but if you're not comfortable implementing your own preemptible kernel / task switcher, particularly one that handles asynchronous (interrupt-triggered) preemption, you can get wrapped around the axle pretty quickly. So what I'm proposing below is not as responsive as a preemption-based kernel, but it's much simpler and often adequate).
Create 3 event/work queues:
- Q1 is the lowest priority and handles your slow, background SD card writes
- Q2 holds requests to process incoming UART packets
- Q3 (highest priority) holds UART RX FIFO read requests.
I split up the UART RX FIFO reading and the processing of the read packet so that the FIFO reading is always serviced ahead of the packet processing; maybe you want to keep them together, your choice.
For this to work, you break your large (~100ms) SD card write process into a bunch of smaller, discrete, run to completion steps.
So for example, to write 5 blocks, 20ms each, you write the first block, then enqueue "write next block" to Q1. You go back to your scheduler at the end of each step & scan the queues in priority order, starting with Q3. If Q2 and Q3 are empty, you pull the next event off of Q1 ("write next block"), and run that command for another 20ms before returning and scanning the queues again. If 20ms is not responsive enough, you break up each 20ms block write into a more fine-grained set of steps, continually posting to Q1 the next work step.
Now for the incoming UART stuff; in the UART RX ISR, you simple enqueue a "read UART FIFO" command in Q3, and return from interrupt back into the 20ms "write block" step that was interrupted. As soon as the CPU finishes the write, it goes back and scans the queues in priority order (worst case response will be 20ms if the block write had just begun at the time of the interrupt). The queue scanner (scheduler) will see that Q3 now has work to do, and it will run that command before going back and scanning again.
The responsiveness in your system, worst case, will be determined by the longest run-to-completion step in the system, regardless of priority. You keep your system very responsive by doing work in small, discrete, run to completion steps.
Note that I have to speak in generalities here. Maybe you want to read the UART RX FIFO in the ISR, put the data into a buffer, and only defer the packet processing, not the actual reading of the FIFO (then you'd only have 2 queues). You have to work this out for yourself. But I hope the approach makes sense.
This event-driven approach with prioritized queues is exactly the approach used by the Quantum Platform (QP) event-driven framework. The QP actually supports an underlying non-preemptive (cooperative) scheduler, such as what was described here, or a preemptive scheduler which runs the scheduler each an event is queued (similar to the approach suggested by SecurityMatt). You can see the code/implementation of the QP's cooperative scheduler over at QP website.