The opposition leader used his budget reply speech on Thursday night to unveil plans to borrow $10 billion for a housing future fund.
Investment returns would pay for 20,000 social houses, including 4000 for women fleeing violence and older women at risk of becoming homeless.
A further 10,000 affordable dwellings would be built for health, emergency services and other frontline workers.
"The security of a roof over one's head should be available to all Australians," he told parliament.
Labor expects 21,500 full-time jobs in construction and the broader economy will be created in the first five years, with a guarantee one in 10 on-site workers will be apprentices.
The Future Fund Board of Guardians would manage the program, with investment returns annually transferred to the National Housing Finance and Investment Corporation.
The returns are also slated to provide $200 million for repairs and improvements on housing in remote Indigenous communities.
Some $100 million would be spent on crisis housing for women fleeing violence and older women at risk of homelessness.
Veterans who are homeless or at-risk of falling into that category would be provided with $30 million in new houses and specialist services.
Federal Housing Minister Michael Sukkar has challenged state and territory governments to do more on social housing after criticism the budget did little to address a growing crisis.
Mr Albanese also pledged $100 million to support 10,000 apprentices who chose to train for jobs in solar, major renewable projects, green hydrogen, energy efficiency home upgrades and renewable manufacturing.
There would be 2500 places annually over four years, with $2000 for starting a qualification, and the same amount each year as well as on completion, capped at $10,000.
The Labor leader took aim at Scott Morrison for saying he didn't hold a hose during the Black Summer bushfires and for pushing quarantine responsibility on to states.
"The prime minister's constant buck-passing and blame shifting has become a handbrake on our economic recovery," Mr Albanese said.
He accused the government of asking voters to forget failures during the coalition's eight years in power as it seeks a fourth term at the next poll, to be held between August and May 21.
"Forget their failures, forget their broken promises, forget all their jobs for their mates," he said.
Make no mistake – the budget handed down on Tuesday night is not a plan for the next generation - it is a patch-up job for the next election.
Responding to Mr Albanese's housing pitch, Mr Sukkar said "Labor will need to more than triple the current benchmark return for the Future Fund of 6.1 per cent to be able to deliver his 20,000 dwellings".
"Labor's policy would only deliver one sixth of the homes at four times the price when compared to the Morrison Government's successful HomeBuilder program," he said.
But the Property Council of Australia welcomed the proposed housing fund.
"Housing affordability is a dire issue for Australia and the Housing Australia Future Fund is an innovative approach to house less fortunate Australians," the council's chief executive Ken Morrison said in a statement.
"We need greater supply across the entire housing spectrum, and this investment would certainly be welcome by the industry."