The speaker spends his time searching for his beloved in their shared home. This person could be the speaker's wife, though the poem never specifies their relationship; still, it's clear that this woman is very important to the speaker. The particulars of her disappearance—where she's gone, why she's gone, even who she is—also remain a mystery, adding to the poem's eerie, mysterious tone.
The diacope of line 1 (the repetition of the word "room") suggests that this search is repetitive and perhaps even endless. This house seems cavernous and maze-like, one room leading to another and then another. The use of the word "inhabit" is also strangely formal; the speaker could have just said that they "live" together. (Maybe he says "inhabit" because this woman is not actually alive!)
Not many people have to "hunt" through their home to find their partner, either. This word adds an element of determination and even aggression to the speaker's search. If he's hunting this woman, does that mean she's "prey"—and trying to escape him? Or is the speaker simply describing how intense this search feels to him? (Interestingly enough, Browning's "Life in a Love," published in the same collection as "Love in a Life," begins with the speaker declaring, "Escape me? / Never—.")
Either way, the breathy alliteration of "hunt" and "house" evokes the desperate, even frantic nature of this search. The enjambment between lines 2 and 3 ("through / We") also might make it feel as though the poem is darting from line to line just as the speaker goes from room to room.
The syntax of these opening lines is pretty strange in general, with the placement of "We inhabit together" at the end of the sentence after the preposition "through." The winding word order here makes the poem a bit harder to follow—perhaps like the elusive lover herself! This word order also allows the poet to place "I" and "We" in the same spot in two separate lines, subtly emphasizing the fact that the speaker ("I") is separate from his partner (he's not part of that "We" right now).