Q) Is marriage a type of relationship that was made by God that shows the relationship between Jesus and Father God?
A) I believe it is. Let’s take a look at the Word of God for examples.
Ephesians 5: 21-33
Submit to one another out of reverence for Christ.
22 Wives, submit yourselves to your own husbands as you do to the Lord. 23 For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior. 24 Now as the church submits to Christ, so also wives should submit to their husbands in everything.
25 Husbands, love your wives, just as Christ loved the church and gave himself up for her 26 to make her holy, cleansing her by the washing with water through the word, 27 and to present her to himself as a radiant church, without stain or wrinkle or any other blemish, but holy and blameless. 28 In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. 29 After all, no one ever hated their own body, but they feed and care for their body, just as Christ does the church 30 for we are members of his body. 31“For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.”32 This is a profound mystery—but I am talking about Christ and the church. 33 However, each one of you also must love his wife as he loves himself, and the wife must respect her husband.
In these verses, Paul compares marriage to our relationship with God. He talks about how husbands and wives should act toward each other and compares that to how Christians and Christ act toward each other.
For example, Paul says that wives ought to submit to their husbands as we submit to Christ. He says that the husband is the head of the home, because we know from other scriptures that the husband and father have been called to lead the family as the household priest. Therefore, it is the husbands role to provide, protect, and prepare those in his care for the matters of earth, and especially to lead them spiritually. Wives ought to submit to this authority God has placed in their lives. This concept is scary to a woman whose husband is not a Godly man and therefore not qualified for her submission. Many men would love to take advantage of a submissive woman, but when the man is doing his job by honoring God, he has earned her trust enough to qualify for submission. The way Christ earned our trust and therefore qualifies for our submission.
Paul goes on to say that the man should lead his wife in a sacrificial way. Honoring her with his life, willing to give it all for her, even if she is unworthy. Paul compares this love to the love of Christ for us. Christ gave his life, at much personal expense, all the while we are unworthy and often ungrateful. Christ was even forgiving those who were driving the nails through his wrists as they were killing him!
I realize this talks more about marriage as a comparison to our relationship with God, whereas you asked about marriage as a comparison to Jesus and the creator God.
These verses in Ephesians focuses more on our relationship with God as manifested in our earthly relationship, especially our most important earthly relationships, family. The Bible often spends more time focusing on our relationship with God and spends much less time describing who God is or how he works. While we do see plenty on who God is and how He works, I believe that the focus is more on our relationship with Him because that is what was most important to God for us to know. He realizes that we would not well understand much about Him, even if He were to explain it in plain english, because He is so far above us, and outside of our ability to perceive. But if we know Him in a relational way, He is able to be known on a higher level, and grants us access to knowing him on the spiritual plane of existence to come, which will be greater than we can comprehend now.
That said, I still believe that marriage is a relationship that helps us to understand God, and his relationship with Jesus better. God is and always was in perfect relationship. He is three persons in one entity, which is far beyond our ability to understand. But it shows that He exists in relationship. We know we are created in His Image. Therefore, it is no wonder that we desire relationship too. Marriage is a unity of two people becoming as one in life, and something that we needed, even as far back as the very first person. We desire relationship, and are fueled by love, because we are made in the image of our creator, who is in essence the perfect example of unified relationship.