User summary, based on information from English Wikipedia:
Melbourne House is/was an Australian game publisher founded in 1980 (?). They were the mother company to the developper Beam Studios. (English Wiki directs both "Beam" and "Melbourne House" to the same page).
In 1987, Melbourne House was sold to Mastertronic in the latter's attempt to secure the budget market.
The developper Beam Studios that obviously wasn't sold in the process (?), continued to release games on other publishers. The developper was then bought in 1999 by Infogrames and was renamed "Infogrames Melbourne House".
Thus, "Melbourne House" was both the original publisher that owned Beam Studios, and also the name that Beam changed to after the Infogrames acquisition. This entry is the original publishing company.