Continued Assistance to Unemployed Workers Act of 2020 This bill extends unemployment assistance to workers who are unemployed due to the COVID-19 (i.e., coronavirus disease 2019) pandemic. Specifically the bill extends through January 31, 2021 (1) Pandemic Unemployment Compensation, (2) Pandemic Unemployment Assistance (PUA), (3) Pandemic Emergency Unemployment Compensation (PEUC), (4) temporary financing of short-time compensation (STC) payments, (5) temporary financing of STC program agreements, (6) full federal funding of the first week of compensable regular unemployment for states with no waiting period, and (7) 13 additional weeks of pandemic emergency unemployment extension compensation. The bill also extends through June 30, 2021 (1) the federal share of payments to states for extended and regular unemployment compensation, (2) the suspension on the accrual of interest on federal payments made to states for assistance with unemployment, and (3) appropriations for the transfer of funds to state accounts in the Unemployment Trust Fund for the reimbursement of certain governmental entities and nonprofit organizations for amounts paid (in lieu of contributions) into such accounts. The bill provides an additional $125 in mixed earner unemployment compensation to recipients of at least $5,000 of self-employment income in the most recent taxable year before the individual applied for regular compensation.