In September 1942 the CPA founded the National Liberation Front, but there were no other parties in it. The NLF had to contend not only with the Italian and later German occupiers, but also with two anti-communist "resistance" movements: the Balli Kombëtar and the Legaliteti movement. The former had members who joined the German puppet regime in 1943, the latter stood in the northern parts of the country waiting for the NLF and Germans to "bleed themselves dry." The NLF liberated Tirana on November 28, 1944. In 1945 the NLF became the Democratic Front. Liberal elements were denounced and expelled in 1946 and a People's Democratic system was proclaimed with extensive land reform and social ownership of the means of production (IIRC about 90% of its was state-owned by 1948.) In 1950 the Party of Labour of Albania (the CPA was renamed it in 1948 at Stalin's request) was declared the leading force of the state.
I read a bit from Chuev's 1970's-80's conversations with Molotov earlier today. According to Molotov Rakosi wanted to be the "Stalin of Hungary" which Molotov said was "too much."
Anyway in 1941 the Communist Party of Albania was formed but it had less than 200 members. It was at once involved in the national liberation war much like Tito's partisans, who helped the Albanian communists fight the Italians and Germans.
My knowledge on Hungary isn't great, but from what I know the establishment of People's Democracy in Hungary was a fair bit less popular than in other countries, even Poland. In his memoirs Enver Hoxha says that the Hungarian leadership was very ineffective at what it did.