In Act I of Othello, the first talk of Desdemona and Othello as a couple comes from Iago as he makes crude remarks about their relationship, insults Othello and suggests that Desdemona is capable of deception. Brabantio is devastated at what he thinks is a travesty and he is intent on confronting Othello. He says, "Fathers, from hence trust not your daughters' minds" (I.i.171), leading the audience to presume that the relationship, indeed marriage, between Othello and Desdemona is most unsuitable.
When Othello is given an opportunity to justify himself, the audience sees a very different picture of a gallant and noble Moor. He tells the Duke and Brabantio that Desdemona "loved me for the dangers I had passed" (I.iii.167). When Desdemona is called to either confirm or deny her love for Othello, she unreservedly proclaims her feelings and her father subsequently accepts them as a couple but not without also issuing a warning about what his daughter may therefore be capable of. He says, "She has deceived her father and may thee" (I.iii.293) to Othello when he leaves.
Othello insists that Desdemona should not be left behind when he sails for Cyprus, and she agrees with him, revealing that they want to start their relationship on a firm footing, supporting each other. The Duke gives the couple his blessing and it is apparent that they cherish each other. Sadly, Iago is already scheming to change that.