According to the USPS, the maximum thickness on a postcard cannot exceed 16-points.
Please note that in order to benefit from USPS Reduced Postage Rate for your postcards, you must use 4OVER4.COM's Direct Mail Templates that have been setup to meet USPS design guidelines. As you will see there are requirements for the size of the inkjet area, bar-code placement, and indicia. Reduced Postage Rates quoted are only available for FULL AUTOMATION orders, which requires that the USPS design guidelines are met.
4OVER4 Uses USPS Reduced Postage Rate to calculate your order. Orders that do not follow USPS Direct Mail Guidelines will be posted at the standard postage rate and will be invoiced accordingly.
https://www.4over4.com/blank-templates/direct-mail-postcards