Who do mainline Protestants believe an "archangel" (such as Michael) to be?

While Mikha'el ("Michael") is referred to as an ἀρχάγγελος ("archangel") in the Greek New Testament (Jude 1:9), some assume that he is the only archangel in existence.

However, Dan. 10:13 states that Mikh'ael is אחד השרים הראשנים, that is, "one of the chief princes," not the chief prince. If Mikh'ael is an "archangel," and also "one of the chief princes," then this equates "archangel" with "chief prince" and implies that there are other archangels. Scripture does not mention them because they're not relevant.

An archangel, in the Protestant definition, is simply an angel with a high rank, often referred to as a "chief" angel. It is believed that they have a higher rank, and power.

Not much else is known for sure, as precious little is found about them in the Bible

As was stated previously, the Bible gives us precious little information about angelic beings - especially the Archangels. We would all like to know more about these extraordinary creatures, yet God has chosen in this present age to disclose very limited knowledge about them. In the kingdom of God, however, all will be made clear to us, including the mystery of the angels:

The understanding isn't significantly different than the Catholic or Eastern Orthodox understanding. The Catholic Encyclopedia article on angels does give a bit more information on what "higher rank" might mean by showing their understanding of the hierarchy:

St. Thomas (Summa Theologica I:108), following St. Denis (De Coelesti Hierarchia, vi, vii), divides the angels into three hierarchies each of which contains three orders. Their proximity to the Supreme Being serves as the basis of this division. In the first hierarchy he places the Seraphim, Cherubim, and Thrones; in the second, the Dominations, Virtues, and Powers; in the third, the Principalities, Archangels, and Angels. The only Scriptural names furnished of individual angels are Raphael, Michael, and Gabriel, names which signify their respective attributes. Apocryphal Jewish books, such as the Book of Enoch, supply those of Uriel and Jeremiel, while many are found in other apocryphal sources, like those Milton names in "Paradise Lost". (On superstitious use of such names, see above).

Archangels, like all angels are created beings. Certain denominations claim that Jesus was an angel, but this is considered a heresy by most Christian denominations, as it denies the divinity of Christ.

Mainline Protestants understand that an Archangel is simply a higher-ranking angel, the prefix "arch" meaning "over". For example, an Archbishop is the "principal" bishop in an ecclesiastical province. Although Michael may be the only named Archangel (in Jude verse 9) that does not mean there are no other Archangels.

With regard to the view held by Jehovah's Witnesses (that Jesus is Michael the Archangel) I found an article that addresses this subject as published in one of their books:

Did John Calvin Really Teach that Jesus was the Archangel Michael?

The main difference between the Protestant view of archangels and angels compared to how Jehovah's Witnesses view Michael the archangel, is that Protestants understand all angels were created, unlike the pre-mortal Jesus who is the eternal and uncreated Word of God who was with God in the beginning and who is God (John 1:1-3, 14).

There is some debate over how many archangels there are. Gabriel is referred to as an archangel by Catholic tradition, but there is no scripture supporting that. The apocryphal 'Book of Enoch' as well as Ephesians 1:21 and Colossians 1:16 was used by Thomas Aquinas and others preceding him, to develop the 'Angelic Hierarchy', but scripture is very vague when it comes to this.

The word "archangel" comes from the Greek αρχάγγελος (archaggělǒs), meaning chief angel, a translation of the Hebrew רב־מלאך (rav-mal'ákh). There are only 2 verses in the NT that say "Archangel", 1 Thessalonians 4:16 and Jude 1:9. They both refer to Michael as the archangel (singular), though Michael is also referred to in the OT, Daniel 10:13-21, as "one of the chief princes" (vs 13) (also translated as chief angels in some translations). So scripture isn't clear as to whether he is one of several/many archangels, or the only one.

It is important to note that Michael is AN angel, and therefore not accorded the same favors that are afforded to Christ (Hebrews 1:5, 2:5), as the author of Hebrews shows how unique the Son of God is, even above the angels, nor will the world be subject to them, unlike Christ, who will reign (Revelation 19:16; Matthew 2:1, 2; 9:35). Also, Jude 1:9 presents Michael as not even have the power to rebuke Satan alone, as he stated "the Lord rebuke you", whereas Christ had the power to rebuke Satan and demons on his own authority (Matthew 4:10, 16:23, 17:18; Mark 8:33; Luke 4:35).