Officers have released CCTV footage of the incident in a bid to identify the pair.
They were caught on camera crossing the tracks at Eastbrook Station, and the man was seen to carry a baby in a pushchair from one side to the other, after getting off the train on platform 1.
It is hoped the footage will serve as a stark warning to others who trespass by taking shortcuts across the tracks.
Inspector Mike Jones, officer in charge at BTP Cardiff, said: "I am genuinely shocked to see that, despite our constant warnings, some people are still willing to risk their lives by trespassing on the tracks.
“Not only that - this footage clearly shows the man and woman pictured had complete disregard for the safety of others as they carried across an infant in a buggy.
"I cannot emphasise enough the dangers associated with this type of mindless behaviour. These two people were extremely lucky that a train was not passing through at the time, otherwise the consequences could have been unthinkable.
“It is staggering that people are still willing to risk everything by entering the railway - doing so with a baby in tow simply defies belief," added Inspector Jones.
“Their behaviour is utterly reprehensible. Parents and adults should be leading by example, taking responsibility and emphasising the dangers to children.
“The few seconds saved by crossing the tracks could end up costing your life. Is it worth it?"
Inspector Jones appealed for the public’s help to identify the people pictured.
Anyone with any information about the incident, which took place at 4.17pm on Tuesday, October 9, is asked to contact British Transport Police on Freefone 0800 40 50 40 quoting background reference B3/WCA of 09/11/2012. Alternatively, call Crimestoppers anonymously on 0800 555 111.