Healthy Climate and Family Security Act of 2019 This bill requires the Department of the Treasury to establish a carbon trading program that caps the emissions of carbon dioxide (CO2) from crude oil, coal, and natural gas. Beginning in 2019, crude oil refineries, petroleum importers, coal mines, coal importers, and natural gas suppliers or processors must purchase carbon permits equivalent to the amount of CO2 that would be emitted by covered fuels. This bill establishes a declining cap on the quantity of permits issued to reduce CO2 emissions until 2040 when the permits issued represent an amount 80% below 2005 CO2 emission levels. This bill provides for the trading or sale of permits between entities, the banking by entities of permits for future years, and the borrowing by Treasury of permits from future years to stabilize permit prices. Auction proceeds and penalties are returned to U.S. citizens lawfully present in the United States using the Healthy Climate Trust Fund established by this bill. Treasury must impose fees on the import and pay fees for the export of carbon-intensive goods when the export country does not have equivalent measures to regulate greenhouse gases. Carbon-intensive goods are goods with an increased cost due to the regulation of greenhouse gases. The Environmental Protection Agency must regulate within 10 years all sources of greenhouse gases that are anthropogenically emitted. This excludes gases attributable to the production of animals for food.