I . . . . . . . . a letter when he came to my house.

'was writing' is the past continuous form.
The Past Continuous is used to denote an action going on at some time in the past.
The time of the action may or may not be indicated.
In the given sentence, the Past Continuous and Simple Past are used together when a new action (he came to my house) happened in the middle of a longer action (I was writing a letter).