DOOM (DOM over OM) implements both the Axiom API and the standard DOM API. To use this implementation, add axiom-dom to your project and request an OMMetaFactory with the DOM feature:
OMMetaFactory mf = OMAbstractFactory.getMetaFactory(OMAbstractFactory.FEATURE_DOM);
You can then get OMFactory and SOAPFactory instances from that OMMetaFactory. All nodes created using these factories will implement both APIs; e.g. you can cast any OMElement to an org.w3c.dom.Element. The exact semantics are documented here.
To parse an existing XML document with DOOM, make sure that you use one of the methods in OMXMLBuilderFactory that take an OMFactory or OMMetaFactory argument.
Finally, if you need to use JAXP/DOM APIs to create an object model, cast the OMMetaFactory obtained by the instruction shown above to a DOMMetaFactory. That API then allows you to create a DocumentBuilderFactory implemented by DOOM.