Career
Džomba began his career by his hometown club RK Zamet, where he stayed until 1996, when he signed to RK Zagreb. He spent five years with the capital team, winning the national championship and cup title in each season. Mirza"s father is called Džafer Džomba.
In addition, he reached the EHF Champions League finals with Zagreb three times in row between 1997 and 1999, however, they fell short to Spanish giants Football Club Barcelona in all three occasions.
In 2001 Džomba moved abroad and joined Hungarian top team KC Veszprém. With the Central Transdanubian club he has obtained both the domestic league and cup title in 2002 and also played the EHF Champions League final, but lost once again, this time against South Carolina Magdeburg.
Following the successes both in the Hungarian championship and the Hungarian cup in the next two years, Džomba got an offer from Bachelor of Medicine Ciudad Real and switched to the reigning Spanish champions in the summer of 2004. The Croatian right wing collected almost all possible clubs titles while at Ciudad Real, including the EHF Champions League, the EHF Champions Trophy and the IHF Super Globe.
On domestic level he acquired the Spanish league gold and the Spanish Supercup.
He left Spain in the summer of 2007 to join his former team RK Zagreb. During his second spell at the club he added further three Croatian league and cup gold to his collection and also had good runs in the Champions League, regularly getting to the knockout phase of the continental tournament. On 15 June 2010 it was confirmed that the Džomba signed a contract with Polish Extraklasa title holders Vive Targi Kielce.
He played one season in Poland, winning the cup and reaching in the league playoff finals, where regular season winners Kielce were beaten 1–3 by Wisła Płock in the best-of-five series.
Džomba announced his retirement from professional handball in August 2011 at the age of 34. Club International.