Ulric was the son of Margrave Poppo I of Carniola and Hadamut, daughter of Count Werigand of Friuli and Istria.
Ulric married Sophia,[1] the daughter of King Béla I of Hungary and his first wife, Richeza, sister of the Polish duke Casimir I the Restorer.
Alternatively, it has been suggested that she was the daughter of Béla and his second wife, Tuta of Formbach, and thereby a sister of King Ladislaus I of Hungary.
She gave her first husband four children: On 31 July 1064, King Henry IV of Germany donated land in pago Histrie ... in comitatu Odalrici marchionis ('in the country of Istria ... in the county of Margrave Ulric') to prefato Odalrico marchioni ('the prefect Ulric, margrave').
A loyal supporter of the Imperial Salian dynasty and backed by his Hungarian brothers-in-law, Ulric was able to enlarge his margraviate down to Fiume, against the resistance of the Patriarchs of Aquileia and the Republic of Venice.