Continuous Health Coverage for Workers Act This bill provides health insurance premium assistance through 2020 for individuals who become unemployed, are furloughed, or receive a reduction in hours. Specifically, the bill treats premiums as paid for individuals who pay a specified minimum amount toward the premium and (1) are terminated from employment and elect to continue insurance coverage through the COBRA (Consolidated Omnibus Budget Reconciliation Act) program, (2) receive a greater than 30% reduction in paid hours but remain eligible for coverage under a group health plan, or (3) have been terminated or receive reduced hours for the duration of time that their employers voluntarily offer coverage under a church health plan. The bill also specifies requirements for individuals changing, or enrolling in, health plans under the program. Additionally, the bill requires employers to provide eligible individuals specified written notice about the premium assistance program, including, among other information, available health plan enrollment options and the date that such assistance expires. The Department of the Treasury must reimburse employers, group health plans, and insurance issuers through a payroll tax credit or refund for unpaid premiums that were treated as paid under the program. Premium assistance is not considered income for federal income tax purposes.