Postal Service Improvement Act This bill requires mail-in ballots for federal elections to meet certain design and tracking requirements and revises authority to provide parental leave to postal employees. Specifically, each mail-in ballot must be carried or delivered in an envelope that contains a USPS barcode that enables tracking of each individual ballot, satisfies USPS requirements for ballot envelope design and for machinable (i.e., able to be processed using USPS equipment) letters, and includes the official election mail logo. The federal government must reimburse each state (including the District of Columbia and any U.S. territory or possession) for the cost of using the barcode service. The bill also provides paid parental leave to officers and employees of the USPS and the Postal Regulatory Commission.