In Julius Caesar, what does Brutus’s encounter with Portia teach you about Portia, about Brutus, and about their marriage?

This is a great question! So many people read Julius Caesar and assume that women have no significant role in the text, but that is not true. The dynamic between Brutus and Portia (and Caesar and Calpurnia) are essential in fully developing both Brutus and Caesar's characters. Without this rounding of their characters, it would be difficult to assess who is the tragic hero of the play.

Brutus's encounter with Portia takes place in their home after Brutus agrees to join the conspiracy to assassinate Caesar. At this point in the play, Brutus admitted that he is "with himself at war" or internally conflicted about his choice to assassinate Caesar. However, he decides that he loves Rome more than he does Caesar, and like the "serpent's egg" will "kill [Caesar] in the shell." He will eliminate the threat before Caesar's ambition is allowed to grow and destroy the Roman Republic. 

Immediately prior to his conversation with Portia, Brutus meets with Cassius, Casca, Decius, and others to discuss the logistics of Caesar's assassination. Although others suggest that the men swear an oath, Brutus objects the idea because he believes that an oath suggests their cause is not honest or noble. Brutus also rejects the idea that Mark Antony be killed because Brutus believes Antony is "but a limb of Caesar." He also doesn't want their cause to seem to "bloody"; he doesn't want any Roman citizen to think they assassinate Caesar out of jealousy or another self-serving motive. Although Brutus leaves the meeting as an established leader of the conspiracy, it does not mean that he still isn't troubled by his decisions. Through his conversation with Portia, it is evident that Brutus has a lot of difficultly with his decision to assassinate Caesar - even if it is for the good of Rome. 

When Portia speaks to Brutus, she reveals to the audience that Brutus is a good husband because of what he isn't doing lately. She informs him that 

You've ungently, Brutus, 
Stole from my bed: and yesternight, at supper, 865
You suddenly arose, and walk'd about, 
Musing and sighing, with your arms across, 
And when I ask'd you what the matter was, 
You stared upon me with ungentle looks; 
I urged you further; then you scratch'd your head, 870
And too impatiently stamp'd with your foot; 
Yet I insisted, yet you answer'd not, 
But, with an angry wafture of your hand, 
Gave sign for me to leave you: so I did; 
Fearing to strengthen that impatience 875
Which seem'd too much enkindled, and withal 
Hoping it was but an effect of humour, 
Which sometime hath his hour with every man. 
It will not let you eat, nor talk, nor sleep, 
And could it work so much upon your shape 880
As it hath much prevail'd on your condition, 
I should not know you, Brutus (II, i, 865-880).

In her recount of Brutus' recent behavior, we learn that he is not acting like himself. Therefore we can deduce that normally he would treat Portia as an equal: discuss matters with her, enjoy his time with her, and treat her with respect. When Brutus tries to deny that something is wrong and he is simply sick, Portia resorts to pleading with him "By all your vows of love and that great vow/ Which did incorporate and make us one," (II, i, 889-900). This implies that Brutus takes his vows seriously and abides by them. It also reveals that Portia feels that she is at liberty to speak to Brutus as an equal, and she does not answer to Brutus as a subordinate. Finally, she tells him that if she is not his equal and their entire marriage was not built on mutual respect, than "Portia is Brutus' harlot, not his wife" (II, i, 915). This is powerful because Portia is not a common harlot. She is "a woman well-reputed" and expects to be treated as such. Portia is not a common female figure in many male dominated plays of this time. She is commands and demands respect. Brutus obliges and declares, "O ye gods, Render me worthy of this noble wife!" (II,i, 931-32)

Through this exchange it is evident that Portia is an important character in the play because she helps to develop Brutus' character. She gives the audience insight to his motives and reinforces the characterization that Brutus is a good, noble, and respectable man. Therefore we can say conclude Brutus is not killing Caesar due to personal animosity or hatred for the man, but that Brutus is honest when he declares he believes Caesar must be killed to preserve the republic.