Please compare bitheism and ditheism.
Some examples may be helpful. While Hinduism is polytheistic because it maintains a belief in 33 main gods and millions of others (see below), it also encompasses bitheism. The two primary gods of Hinduism are Vishnu (preserver) and Shiva (destroyer & transformer). Within this false religion both of these gods are seen as coming forth from the one god Brahma (creator). They are not in opposition to one another but are seen rather to bring about things together; or it can be said that they are also considered essentially the same god moving in two different forms (i.e. preserver & destroyer).
On the other hand, another false religion called Zoroastrianism (or Mazdaiam) believes in one universal, transcendent, supreme god, but is ditheistic. Zoroaster (aka: Zarathustra, Zarathushtra Spitama, or Ashu Zarathushtra) in his writings called Zend-Avesta, essentially taught the idea of a continuous struggle between Ormazd (the god of creation, light, and goodness) and his enemy Ahriman (the god of evil and darkness). So, in this form of dualism there are two opposite and opposing forces, or gods.
Diametrically opposed to all forms of dualism, the God of Christianity and all creation is monotheistic; it asserts the truth that there is one and only one God. In the Shema, the Bible states, "Hear, O Israel: The Lord our God, the Lord is one" (Deut. 6:4). However, Deuteronomy 6:4 also embraces the doctrine of the Trinity (three persons, one essence). The Hebrew word for "one" is echad, which refers to one, not in the absolute sense but one in the collective sense, like one bunch of grapes.
We see a plural number of persons in the Godhead as early as Genesis 1 when God said let "us" make man in our own image (Gen. 1:26; cf. Gen. 3:22; 11;7; Isa. 6:8; Matt. 3:16-17; 28:19; 1 Cor. 12:4-6; 2 Cor. 13:14; Eph. 4:4-6; 1 Pet. 1:2; Jude 1:20-21). Indeed, the word used for God in Genesis 1:1 is Elohim. This is a form of the Hebrew word El. In the Hebrew language, the "im" ending indicates a plurality. Therefore, Elohim is the plural form of El. So, from the very first verse of the Bible forward we observe the doctrine of the Trinity.
In the ontological Trinity, there is one God in three persons — God the Father, God the Son, and God the Holy Spirit. The Son and the Spirit are equal to the Father in power, glory, and being (John 1:1; 1 Cor. 6:19, etc.). All three persons within the Godhead are equal in nature, essence, and their attributes (omniscience, omnipresence, omnipotence, holiness, etc.).
In addition, Satan and God are not equal forces. While the three members of the Trinity are each distinct persons in the eternal Godhead, Satan is merely a fallen angel — he is a created being and not Creator God. So, God is sovereign and infinitely greater than Satan:
God is indeed sovereign over all the earth. He is sovereign over all, even over such miracles as the time of the cross — and every other person, event, minute, and second — over all creation. He does everything he pleases (Exod 15:18; 1 Chron 29:11-12; 2 Chron 20:6; Psa 22:28); while retaining the right to control all things he actually and actively ordains and brings to pass everything that takes place in entire universe (Deut 32:39; 1 Sam 2:6-8; Job 9:12; 12:6-10; Psa 33:11; 115:3; 135:6; Isa 14:24; 45:7; Acts 15:17-18; Eph 1:11); he controls the simple roll of a dice (Prov 16:33), to the greatest events of the earth (e.g. Isa 45:1-4); he is bringing all things to pass according to his will. He governs and superintends "coincidental" happenings (1 Kings 22:20, 34, 37), the wicked actions of men (Gen 45:5; 50:20; Exod 4:21; Judges 14:1-4; Psa 76:10; Prov 16:4; 21:1; Isa 44:28; Amos 3:6; Acts 2:22-23; 4:27-28), men's good deeds (John 15:16; Eph 2:10; Phil 2:12-13), the actions of both evil spirits and good angels (1 Sam 16:14-16; 1 Kings 22:19-23; 1 Chron 21:1; 2 Sam 24:1; Psa 103:20-21; 104:4), the habits of animals (Num 22:28; 1 Kings 17:4; Psa 29:9; Jer 8:7; Ezek 32:4; Dan 6:22), and the operations of all creation (Gen 8:22; Psa 104:5-10, 13-14, 19-20; Mark 4:39). God is absolutely sovereign over all, including Satan and his host. Indeed, Satan must ask permission from God to do what he does (cf. Job 1:6-12). Satan is a liar and deceiver (cf. John 8:44; Rev. 12:9). Though the epitome of darkness (cf. Col.1:13) he masquerades as an angel of light (2 Cor. 11:4). The saints upon the throne with Christ (2 Tim. 2:12; Rev. 3:21) and participating in the rights and the authority of Jesus (John 5:27; Eph. 2:22-23) will judge angels (1 Cor. 6:3). Ultimately at the last day, Satan will be cast into an eternal hell (Matt. 25:41). So, while God and Satan are opposing forces, they aren't in anyway equal or complimentary.The Bible does not teach bitheism or ditheism. All forms of dualism are misleading beliefs taught by false prophets.
Dr. Joseph R. Nally, Jr., D.D., M.Div. is the Theological Editor at Third Millennium Ministries (Thirdmill).