Appalachian Communities Health Emergency Act or the ACHE Act This bill places restrictions and requirements on certain mining projects until the Department of Health and Human Services (HHS) determines whether such projects pose risks to human health. The bill applies to mountaintop-removal coal mining projects that use blasting with explosives in the steep slope regions of Kentucky, Tennessee, Virginia, and West Virginia. Specifically, the bill requires the National Institute of Environmental Health Sciences to conduct or support studies on the health impacts of mountaintop-removal coal mining projects on individuals in the surrounding communities. HHS must use these studies when making its determination on whether such mining presents any health risks to those individuals. Until HHS makes its determination, entities carrying out such mining must monitor levels of soil, water, air, and noise pollution. HHS must make the results of this monitoring publicly available. In addition, specified agencies may not issue permits for any mountaintop-removal coal mining project or expansion unless HHS determines that such mining does not present any health risk to individuals in the surrounding communities. The Office of Surface Mining Reclamation and Enforcement of the Department of the Interior must assess a one-time fee upon existing mining projects. The fee must cover the federal cost of the studies and pollution monitoring required by the bill.