Can I use Babel to transpile both ECMA and Typescript?

Question

I have a simple project with 2 tests.

test.jsx
test.tsx

When I run mocha with the following presets

"presets": ["@babel/preset-env", "@babel/preset-react"]

The jsx test works but the tsx has a problem parsing...

(function (exports, require, module, __filename, __dirname) { import React from
'react';
                                                                     ^^^^^

SyntaxError: Unexpected identifier

When I change to...

"presets": ["@babel/preset-typescript", "@babel/preset-react"],

I get

I:\...\enzyme-example-mocha\test\.setup.js:1
(function (exports, require, module, __filename, __dirname) { import { JSDOM } f
rom 'jsdom';
                                                                     ^

SyntaxError: Unexpected token {

Is there a way I can get both to work? My project is based off of

https://github.com/airbnb/enzyme/tree/master/packages/enzyme-example-mocha

I also tried

["@babel/preset-typescript", "@babel/preset-env", "@babel/preset-react"]

But I get the same...

I:\...\enzyme-example-mocha\test\.setup.js:1
(function (exports, require, module, __filename, __dirname) { import { JSDOM } f
rom 'jsdom';

If I switch around ["@babel/preset-env", "@babel/preset-typescript", "@babel/preset-react"] I get

(function (exports, require, module, __filename, __dirname) { import React from
'react';
                                                                     ^^^^^

SyntaxError: Unexpected identifier