She is married to Adolf II von Berg.
They got married
Child(ren):
daughter . The Chronicle of Alberic de Trois-Fontaines names "comitissa Mathildis Campaniensis et uxor Renaldi comitis Nivernensis et comitissa Montis Veteris iuxta Coloniam et mater illorum Romanorum qui Froiepain dicuntur" as sisters of "archiepiscopi Coloniensis Frederici"[143]. In the case of the two sisters named first, other sources confirm that they were daughters of Engelbert Marchese of Istria, Duke of Carinthia. It is possible therefore that the other two named sisters (of which the countess of Berg was one) were also Engelbert’s daughters. Ascertaining the precise family relationship between all four presumed sisters and Friedrich [I] Archbishop of Köln depends on interpreting apparently contradictory sources which link the archbishop with the Sponheim and Schwarzenberg/Regensberg families, a problem which is discussed in detail in the document BAVARIA NOBILITY. Europäische Stammtafeln indicates that Adolf [II]’s second wife was the daughter of Engelbert, son of Berthold [I] [von Schwarzenberg][144]. No primary source has been identified which confirms that this is correct: it is presumably consistent with another theory about the origin of Archbishop Friedrich. m as his second wife, ADOLF [II] Graf von Berg, son of ADOLF [I] Graf von Berg & his wife Adelheid von Laufen (-12 Oct after 1160).]
Bronnen:
[143] Chronica Albrici Monachi Trium Fontium 1150, MGH SS XXIII, p. 840.
[144] ES XVIII 2 and ES XVI 80 A.
https://fmg.ac/Projects/MedLands/CARINTHIA.htm#IrmgardMAdolfIIBerg