MIAMI (AP) _ Eastern Airlines sued two of its unions for $1.5 billion Friday, accusing pilots and machinists of ''Eastern-bashing'' to drive down the carrier's value so they could buy it cheaply on the stock market.

In the latest in a series of labor-management battles at the ailing airline, Miami-based Eastern and parent company Texas Air Corp. alleged that the International Association of Machinists and the Air Line Pilots Association ''have campaigned to smear'' them.

''The smear campaign is one of a number of tactics to facilitate a takeover,'' airline attorney Parker Folse III of Houston said.

Also Friday, Texas Air reported a $124.3 million loss for the first three months of 1988 on revenues of $2.1 billion, vs. a loss of $101 million on revenues of $2 billion for the same period a year ago. Eastern had a $31 million loss for the first quarter, compared with net income of $2.1 million in the same period in 1987.

Eastern's ALPA chairman, John Bavis, among those named individually in the federal court suit, brushed it off as a company tactic to divert attention from a U.S. Department of Transportation probe of the carriers' finances and safety.

''This is like the lions suing the Christians for animal abuse. The situation at Eastern today has been called the corporate version of the battered child syndrome - with the company being mugged by its own parent, Texas Air,'' Bavis said.

Machinist local President Charles Bryan said in Atlanta that the lawsuit was an effort to shift public opinion.

''It's clear evidence of a last-ditch effort by a very desperate man, and that man's Frank Lorenzo,'' he said of Texas Air's owner. The suit is ''a typical gesture on his (Lorenzo's) part, to blame others for his problems.''

ALPA President Henry Duffy called the Eastern suit ''a desperate attempt to draw attention away from Texas Air's and Eastern's growing problems.''

Duffy said the suit ''dredges up some pretty thin items'' and cited a reference by Eastern to an alleged union pamphlet critical of the airline.

''The pamphlet ... was authored some 10 years ago by an individual pilot acting on his own, who has long since retired from flying,'' Duffy said in a statement issued in Washington by the 40,000-member union.

ALPA, the IAM and Eastern's Transport Worker Union tried to buy the carrier before Texas Air bought it in 1986 for $676 million, a sale the unions then tried to block. The suit says the two unions still hope to obtain Eastern, which has lost $900 million in the last 10 years.

''They seek this by an all-out effort to injure Eastern's business - to make it a financial millstone for Texas Air - by means of ... mail fraud, wire fraud, extortion. ... Further, they have set out to destroy Eastern's good will and reputation,'' the suit said.

The suit also said that ''by promoting deceitful accusations about the safety of Eastern, defendants have induced the news media to join in an 'Eastern-bashing' effort, and have led the DOT (Department of Transportation) and the FAA (Federal Aviation Administration) to conduct costly investigations of the airline, all of which have further damaged Eastern's business.''

''Indeed, that is the precise objective of the smear campaign - to drain Eastern of its economic vitality, and to continue draining it until either Texas Air delivers the company into union hands or Eastern is driven into bankruptcy.''

If unable to obtain Eastern, the pilots and machinists ''are prepared to destroy both companies,'' says the suit, which notes the labor groups have consulted with T. Boone Pickens on a plan to take over Texas Air for $1.2 billion.

The suit is baseless, said John Edmond, a Washington lawyer for the machinists. Their contract dispute with Eastern - which seeks wage cuts of up to 50 percent - is in federal mediation.

The unions have long contended that Texas Air and Lorenzo aim to strip Eastern of its assets and bust its unions. The suit filed Friday in Miami is another example, said Mary Jane Barry, president of the TWU, which represents about 7,000 flight attendants and is not named in the suit.

''It's just another way to deplete the unions' treasury, to keep them in court. I think everything Lorenzo does is a divide-and-conquer tactic,'' said Ms. Barry. ''Everything he does is to dismantle the company. He's going to get rid of the unions in some manner.''

ALPA's Bavis said the suit merely aims to divert attention from the federal probes of Eastern, Texas Air and another of its subsidiaries, Continental Airlines.

Last month, the FAA announced it was seeking $823,000 in penalties from Eastern for past safety violations and it then began a plane-by-plane inspection of the carrier. Last year, Eastern paid a $9.5 million fine for violations.

The House Public Works and Transportation Committee approved a non-binding resolution Thursday urging DOT, parent of the FAA, to widen the probe of Eastern and Texas Air to include how the public and workers might be affected by company policies.