This week's Haftarah is generally read twice a year. The special Shabbos Rosh Chodesh Haftarah comes from the concluding chapter of Yeshayahu (66:1-24). The Levush (425:2) and the Mishnah Berurah (425:4) both explain the connection from Rosh Chodesh to the Haftarah.
The second to last verse of the Haftarah speaks of the honor given to Hashem on Rosh Chodesh monthly. On Shabbos weekly: And it shall be that, at every new moon and on every Shabbos, all humanity will come to prostrate themselves before me, says Hashem.
Since this verse speaks of both Shabbos and Rosh Chodesh, it is an appropriate Haftarah to read each Rosh Chodesh that falls on Shabbos.