The relationship between Macbeth and Banquo is presented first. They seem to be good friends. They are walking together after the battle, and they laugh and joke about the witches’ prophecies.
At this point, the prophecy is not a point of contention between them. Macbeth clearly takes it seriously though, and soon Banquo seems to be worried about him.
That, trusted home,(130)
Might yet enkindle you unto the crown,
Besides the Thane of Cawdor. But ’tis strange;
And oftentimes, to win us to our harm,
The instruments of darkness tell us truths,
Win us with honest trifles, to betray's(135)
In deepest consequence— (Act 1, Scene 3, p. 15)
Banquo and Macbeth have a parting of ways when Macbeth becomes king. Banquo suspects that Macbeth killed Duncan to get the spot, and Macbeth suspects that Banquo knows. Macbeth decides to have Banquo killed.
Another relationship is the one between Duncan and Macbeth. They are not close, but they are related and Macbeth has always been loyal to Duncan. Macbeth is convinced by his wife to kill Duncan, but then has second thoughts.
He hath honor'd me of late, and I have bought(35)
Golden opinions from all sorts of people,
Which would be worn now in their newest gloss,
Not cast aside so soon. (Act 1, Scene 7, p. 23)
Duncan trusts Macbeth completely. He has no reason to suspect him.
Give me your hand;
Conduct me to mine host. We love him highly,(35)
And shall continue our graces towards him.
By your leave, hostess. (Act 1, Scene 6, p. 22)
Duncan has not been a bad king. There is no reason to unseat him. At the same time, Macbeth knows that they are kinsman and Duncan. He attempts to back out of the killing Duncan, which brings us to the next important relationship—Macbeth and Lady Macbeth.
Lady Macbeth is definitely the dominant one in this partnership. She accuses her husband of being too kind, and of being a coward, when he does not want to kill Duncan. She is able to convince him. When he asks if their frame will work, and they will not be suspected, she scoffs at him.
Who dares receive it other,
As we shall make our griefs and clamor roar
Upon his death? (Act 1, Scene 6, p. 24)
There is not a lot of affection exchanged between the Macbeths. They seem to be all business. They are not even really that happy to see each other, except to discuss their bloody business.