Allowed to mount Legal defense, face his accuser, have legal representation throughout process. Lots of things he is being denied.
"...nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law..".
Sixth Amendment:
"In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the assistance of counsel for his defense."
The "proceedings" in the House, although they are contemptible and border on revolution in intent if not in fact are perfectly legal and do not violate any part of the US Constitution.
An impeachment by the House of Representatives is most similar to a Grand jury indictment, and as you should know, if you are the subject of a Grand Jury proceeding you have none of the rights described above in the fifth and sixth amendments.