diff --git a/packages/rehype-mathjax/browser.js b/packages/rehype-mathjax/browser.js
index b88a8ba..a1bd647 100644
--- a/packages/rehype-mathjax/browser.js
+++ b/packages/rehype-mathjax/browser.js
@@ -36,4 +36,5 @@ const rehypeMathJaxBrowser =
       }
     )
   )
+
 export default rehypeMathJaxBrowser
diff --git a/packages/rehype-mathjax/lib/create-adaptor.browser.js b/packages/rehype-mathjax/lib/create-adaptor.browser.js
index 8096f1f..cd44dfc 100644
--- a/packages/rehype-mathjax/lib/create-adaptor.browser.js
+++ b/packages/rehype-mathjax/lib/create-adaptor.browser.js
@@ -1,3 +1,3 @@
 import {browserAdaptor} from 'mathjax-full/js/adaptors/browserAdaptor.js'
 
-export {browserAdaptor}
+export {browserAdaptor as createAdaptor}
diff --git a/packages/rehype-mathjax/lib/create-input.js b/packages/rehype-mathjax/lib/create-input.js
index 78e6f5d..30b3d00 100644
--- a/packages/rehype-mathjax/lib/create-input.js
+++ b/packages/rehype-mathjax/lib/create-input.js
@@ -1,8 +1,14 @@
+/**
+ * @typedef {import('mathjax-full/js/util/Options.js').OptionList} OptionList
+ * @typedef {import('mathjax-full/js/input/tex.js').TeX<HTMLElement, Text, Document>} TeX_
+ */
+
 import {TeX} from 'mathjax-full/js/input/tex.js'
 import {AllPackages} from 'mathjax-full/js/input/tex/AllPackages.js'
 
 /**
- * @param {unknown} options
+ * @param {OptionList} options
+ * @returns {TeX_}
  */
 export function createInput(options) {
   return new TeX(Object.assign({packages: AllPackages}, options))
diff --git a/packages/rehype-mathjax/lib/create-output-chtml.js b/packages/rehype-mathjax/lib/create-output-chtml.js
index afc725b..cb6fdd9 100644
--- a/packages/rehype-mathjax/lib/create-output-chtml.js
+++ b/packages/rehype-mathjax/lib/create-output-chtml.js
@@ -1,9 +1,14 @@
+/**
+ * @typedef {import('mathjax-full/js/util/Options.js').OptionList} OptionList
+ * @typedef {import('mathjax-full/js/output/chtml.js').CHTML<HTMLElement, Text, Document>} CHTML_
+ */
+
 import {CHTML} from 'mathjax-full/js/output/chtml.js'
 
 /**
- * @param {unknown} options
+ * @param {OptionList} options
+ * @returns {CHTML_}
  */
 export function createOutputChtml(options) {
-  // @ts-expect-error: assume options work (mathjax types are not exported)
   return new CHTML(options)
 }
diff --git a/packages/rehype-mathjax/lib/create-output-svg.js b/packages/rehype-mathjax/lib/create-output-svg.js
index 7fcc71c..c2763f4 100644
--- a/packages/rehype-mathjax/lib/create-output-svg.js
+++ b/packages/rehype-mathjax/lib/create-output-svg.js
@@ -1,9 +1,14 @@
+/**
+ * @typedef {import('mathjax-full/js/util/Options.js').OptionList} OptionList
+ * @typedef {import('mathjax-full/js/output/svg.js').SVG<HTMLElement, Text, Document>} SVG_
+ */
+
 import {SVG} from 'mathjax-full/js/output/svg.js'
 
 /**
- * @param {unknown} options
+ * @param {OptionList} options
+ * @returns {SVG_}
  */
 export function createOutputSvg(options) {
-  // @ts-expect-error: assume options work (mathjax types are not exported)
   return new SVG(options)
 }
diff --git a/packages/rehype-mathjax/lib/create-renderer.js b/packages/rehype-mathjax/lib/create-renderer.js
index 50e19ea..b953444 100644
--- a/packages/rehype-mathjax/lib/create-renderer.js
+++ b/packages/rehype-mathjax/lib/create-renderer.js
@@ -1,9 +1,8 @@
 /**
  * @typedef {import('hast').Element} Element
- * @typedef {import('mathjax-full/js/core/OutputJax').OutputJax<any, any, any>} OutputJax
+ * @typedef {import('mathjax-full/js/core/OutputJax').OutputJax<HTMLElement, Text, Document>} OutputJax
+ * @typedef {import('mathjax-full/js/core/MathDocument.js').MathDocument<HTMLElement, Text, Document>} MathDocument
  * @typedef {import('./create-plugin.js').CreateRenderer} CreateRenderer
- *
- * For some reason MathJax types can’t be imported.
  */
 
 import {mathjax} from 'mathjax-full/js/mathjax.js'
@@ -34,13 +33,16 @@ RegisterHTMLHandler(adaptor)
  */
 export function createRenderer(inputOptions, output) {
   const input = createInput(inputOptions)
+  /** @type {MathDocument} */
   const doc = mathjax.document('', {InputJax: input, OutputJax: output})
 
   return {
     render(node, options) {
-      const domNode = doc.convert(toText(node), options)
-      // @ts-expect-error: assume no `doctypes`
-      node.children = [fromDom(domNode)]
+      // @ts-expect-error: assume mathml nodes can be handled by
+      // `hast-util-from-dom`.
+      const domNode = fromDom(doc.convert(toText(node), options))
+      // @ts-expect-error: `fromDom` returns an element for a given element.
+      node.children = [domNode]
     },
     styleSheet() {
       const value = adaptor.textContent(output.styleSheet(doc))
diff --git a/packages/rehype-mathjax/package.json b/packages/rehype-mathjax/package.json
index 19d5378..2e1a654 100644
--- a/packages/rehype-mathjax/package.json
+++ b/packages/rehype-mathjax/package.json
@@ -50,6 +50,7 @@
   "dependencies": {
     "@types/hast": "^2.0.0",
     "@types/mathjax": "^0.0.36",
+    "@types/web": "^0.0.15",
     "hast-util-from-dom": "^4.0.0",
     "hast-util-to-text": "^3.0.0",
     "jsdom": "^16.0.0",