I'm receiving unemployment insurance in California. I have a job with my partner, but the checks go to him...?

I have verified that he will be the only one paying taxes on the money we make with this job. However, we have told the management company overseeing us that we will be reporting my hours worked to EDD because they want everything to be done legitimately. But if I am not paying any taxes on the income at all, can I report it as work to EDD? If no... I would obviously like to report I am working less... but the company has asked me to report a certain amount... so I guess the legitimate response would be to have them split our pay into two checks so I have to pay taxes on my part too. Any thoughts from people with experience?