International Airlines Group (IAG), which was formed from the merger of the two airlines in 2011, posted operating losses of 150 million euros (£122.6 million), compared with 278 million euros a year earlier.
BA's loss during the industry's seasonally quiet first quarter was 5 million euros (£4 million), against 72 million euros in 2013, while Iberia almost halved its losses from last year with a deficit of 111 million euros (£90.7 million).
One factor in BA's improvement has been the cost benefit achieved from the performance of its new Airbus A380 and Boeing 787 aircraft.
The airline said Iberia's restructuring remains "a work in progress" but pointed out that today's figures do not include the impact of recent pay and productivity agreements which took effect in April. It is gradually resuming some routes, including long-haul services to Santo Domingo and Montevideo.
Shares opened more than 1% higher today as IAG said it expects to improve operating profits for 2014 by at least 500 million euros (£408.6 million).
The group has around 430 aircraft in service and employs more than 60,000 people. Iberia's restructuring programme has seen 2,500 staff leave the airline under a voluntary redundancy programme, while salaries have been reduced.