The majority position in Reformed theology is that man has two substantial natures – a material body and an immaterial soul – and that the words "soul" and "spirit" are best understood as both referring to the immaterial soul. Berkhof (Systematic Theology, 2.1.2) summarizes the biblical evidence this way:

Trichotomists seek support in the fact that the Bible, as they see it, recognizes two constituent parts of human nature in addition to the lower or material element, namely, the soul (Heb., nephesh; Greek, psuche) and the spirit (Heb., ruach; Greek, pneuma). But the fact that these terms are used with great frequency in Scripture does not warrant the conclusion that they designate component parts rather than different aspects of human nature. A careful study of Scripture clearly shows that it uses the words interchangeably. Both terms denote the higher or spiritual element in man, but contemplate it from different points of view.

He then discusses the way these "different points of view" are expressed:

The main Scriptural distinction is as follows: the word "spirit" designates the spiritual element in man as the principle of life and action which controls the body; while the word "soul" denominates the same element as the subject of action in man, and is therefore often used for the personal pronoun in the Old Testament [...]. In several instances it, more specifically, designates the inner life as the seat of the affections.

With respect to "soul and spirit" proof texts, he points out that other passages, like Matthew 22:37, name even more things (like heart and mind), but this doesn't prove that each is a separate substance. On 1 Thessalonians 5:23 in particular, he writes:

In I Thess. 5:23 the apostle simply desires to strengthen the statement, "And the God of peace Himself sanctify you wholly," by an epexigetical statement, in which the different aspects of man's existence are summed up, and in which he feels perfectly free to mention soul and spirit alongside of each other, because the Bible distinguishes between the two. He cannot very well have thought of them as two different substances here, because he speaks elsewhere of man as consisting of two parts, Rom. 8:10; I Cor. 5:5; 7:34; II Cor. 7:1; Eph. 2:3; Col. 2:5

And on Hebrews 4:12:

Heb. 4:12 should not be taken to mean that the word of God, penetrating to the inner man, makes a separation between his soul and his spirit, which would naturally imply that these two are different substances; but simply as declaring that it brings about a separation in both between the thoughts and intents of the heart.

Charles Hodge also defends the dual nature of man (ST, 2.2.1), and on these passages he writes:

When Paul says to the Thessalonians, “I pray God your whole spirit, and soul, and body, be preserved blameless unto the coming of our Lord Jesus Christ” (1 Thessalonians v. 23). he only uses a periphrasis for the whole man. [...] Again, when in Heb. iv. 12, the Apostle says that the word of God pierces so as to penetrate soul and spirit, and the joints and marrow, he does not assume that soul and spirit are different substances. The joints and marrow are not different substances. They are both material; they are different forms of the same substance; and so soul and spirit are one and the same substance under different aspects or relations. (2.2.2)

Reformed Baptist Wayne Grudem makes similar arguments in his Systematic Theology, chapter 23. He sees Paul "piling up synonyms for emphasis" in 1 Thessalonians 5, and that the author of Hebrews is using multiple terms to describe the "deep inward parts of our being that are not hidden from the penetrating power of the Word of God."

Some, like John Frame, tend more toward monism than the preceding authors, saying that each of the three terms (spirit, soul, and body) "refers to the whole person from a particular perspective." With this understanding, the use of these terms in 1 Thessalonians and Hebrews is explained as follows:

Biblical writers multiply such terms so as to describe the completeness and fullness of human nature. These passages do not make precise distinctions between the terms—certainly not precise enough to define metaphysical components of human existence. Scripture typically uses "spirit" and "soul" interchangeably. (ST, 801)

Summary

In Reformed theology, the most common view is that man has two natures – body and soul. If "spirit" and "soul" are distinguished, they are seen to be aspects of a single nature that are used to emphasize different aspects of the single immaterial part of man.