Can a caregiver get unemployment benefits and IHHS monies for caregiving at the same time?

Nope.

Unemployment is supposed to be temporary and exclusively for people actively looking for AND able to accept work. Caregiving is a lot of work, and if you are compensated for it , it becomes a job. So no you cannot have the taxpayers pay you to do a job AND pay you to be unemployed at the same time.

Generally the above responses are correct. However, it is possible to be working and earning less than what you are eligible to on unemployment and get a portion of your unemployment. It's to encourage you to work at least some. The unemployment does not subtract dollar for dollar. In NV 25% of your earnings are not considered against your benefits.

The poster is in California where one of the requirements for unemployment is "Be available for work which means to be ready and willing to immediately accept work.".
If you are caregiving you are likely not looking for work much less available to accept work.

When you have already accepted work and it's paying less than your unemployment you can still get part of your unemployment. I did it in NV, working as many hours as I could get on the job I had, supplementing it with Unemployment. You are not supposed to be discouraged from working at all by being totally disqualified for some small job.

Try a google search for part time employment and collecting unemployment. Many people could qualify if their hours get cut back. Live and Learn.