Forward is packed with these, especially in the first story arc. One of the more potent ones is when Jayne and River are being tortured by Niska, and he manages to grab her hand and hold it to keep her from breaking. Or any scene between them while they are escaping Niska's ship, with Jayne forced to carry her on his back. Later on in the 3rd arc, where Mal tries to comfort River after she has a mental breakdown after killing Ott's pirates.
"Say again?" he asked.
"Home," she said, and she started crying into his neck, her body shivering with sobs. "I want to go home, Jayne."
"Me too," he hissed, and started out the door with the featherweight of little crazy person on his back. Pistol leading, Jayne Cobb stepped out of that hell chamber, and started their escape.
He was gonna get her out of here, safe and sound, even if the whole gorram Alliance stood in his way.