On the federal section of your return, you will only enter the 1095-A form. You won't input the 1095-B, since there's no place or requirement to enter it. You might need the 1095-B for your state if required. Most states will only ask if you had health insurance for the whole year. They won't ask for any more information.
The 1095-B form is for informational purposes to indicate you had coverage for those months.
The Market Place Health Insurance, which issues the 1095-A, will send a copy of that form to the IRS. If for some reason the information that they send to you is different than what they send to the IRS, the IRS will contact you via letter to request additional information.