Antonio and Bassanio appear to have a family connection, since Salanio refers to Bassanio as Antonio's "most noble kinsman." This, however, is secondary to their deep friendship, to which Antonio immediately alludes as soon as he realizes that Bassanio is going to ask him for money:
My purse, my person, my extremest means,
Lie all unlock'd to your occasions.
This is something more than ordinary friendship and is closer to a marriage vow, in which the couple declare that all their possessions are held in common. It is clear that Bassanio has borrowed money from Antonio before without paying it back, but Antonio remains eager to lend or, indeed, to give his friend whatever he needs. His only reproach is that Bassanio is not more direct and confident in asking for his help, knowing the love Antonio has for him.
You know me well, and herein spend but time
To wind about my love with circumstance;
And out of doubt you do me now more wrong
In making question of my uttermost
Than if you had made waste of all I have.
Again, this is more than ordinary friendship, and Antonio's language sometimes leads audiences to question the nature of the friendship between the two men. As in ancient Greece, intense romantic relationships between men were common in Elizabethan England, meaning that Shakespeare would not have thought of Antonio's love for Bassanio as "homosexual" (a word which did not exist at the time). There is no indication of a physical relationship between the two, and Bassanio is actually asking for his friend's help in pursuing a woman.
It also seems that Antonio's feelings are deeper and stronger than Bassanio's. The relationship might, therefore, be characterized as a deep and passionate friendship in which Antonio is the more emotionally invested. Bassanio, while he loves his friend, is less emotionally attached but is, to some extent, materially dependent on Antonio.