It depends on the era and the monarchy concerned. I will use England as a major example for this. Before the ascension of Henry VIII, the concept of a female ruler was barely ever considered, and was looked down upon as a point of disaster after the wars related to Empress Matilda's right to the throne. Henry VII himself, many believed should have ruled in the right of his wife, Elizabeth of York, who many claimed has more of a right to the throne than he did considering she was the daughter, niece, and sister of Kings of England. But at the time this was disregarded, not even Margaret Beaufort took any claim herself, transferring it to Henry VII, her line from Duke of Lancaster being his claim to the throne.

Henry VIII was interesting in that he officially recognized a woman's right to the throne, and encouraged his daughters to have an intensified education almost equal to their brother's, Edward VI. Of course this did not stop him from wanting a son. When Mary I eventually took the throne, she set the precedent of what the future English monarchy wanted to avoid. She made a unwise choice in marrying the at the time, Prince of Spain, son of Charles V, Philip, who eventually became the king of spain. When they married they became the King and Queen of England and Spain. This was highly unpopular, and the King Philip didnt waste time trying his utmost to use the English monarchy for his own plans. He tried many time to exact his right as a husband to Mary's throne but was put down by her council and he eventually gave up. Mary's constant desire to give her husband support against the French eventually lead to the loss of Calais, the last English stronghold in France which upset many people. When she died there still wasnt a system to what rights a husband of a Queen Regent had? But the one thing that the English knew was that they wanted to avoid what Mary I did. Mary Queen of Scotts shows the same type of unsureness with regards to the title of the husband. When she married her second husband, he constantly tried to say that he was the true King of Scotland as her husband and upset the lords by his angry behavior. His downfall and the major distrust of the nobles led to a severe need to put a check in place for many husbands of Queen Regents. The only exception I can make is that of William and Mary who ruled jointly.

After them most governments in England tried to restrict the influence and power of the Prince-Consort, and refused to give them the title of King, so to not impede on the authority and the higher rank of the Queen Regent herself. So traditionally, the Prince Consort is restricted in his powers, and if his wife/Queen were to die and leave their child a minor as successor, the Consort, with the approval of the government, would act as Regent until the heir comes of age, but would not be seen as the King. All this is to ensure the direct line of power would only be dependent on the line of the Queen Regent and would not

The times when the consort was considered a joint ruler or ruler in place of the queen really depended on the times and region. In Castille in 1400s, Isabella I married Ferdinand of Aragon and they worked as joint rulers specifically. But when she died the right transferred from her daughter, and Ferdinand didnt hesitate to have his widowed daughter moved to a convent imprisoned so that he may rule in her right as King of Castille and when he died Charles V did the same to his mother as a "ruler in her name". Most institutions after watching example of history have avoided granting power to the consort male to make sure he doesnt try and use his wife's hereditary right to take power for himself. I hope that makes sense? Thanks