I found a solution. Instead of using jQuery's fadeIn/fadeOut, start with opacity 0 and visibility hidden, and add a class that has opacity 1 and visibility visible on mouseenter.
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<style>
.child {
-webkit-transition: all 0.4s ease-in-out 0s;
-moz-transition: all 0.4s ease-in-out 0s;
-ms-transition: all 04s ease-in-out 0s;
transition: all 0.4s ease-in-out 0s;
visibility: hidden;
opacity: 0;
}
.child-show {
visibility: visible;
opacity: 1;
}
</style>
</head>
<body>
<div class="parent" style="background:gray; padding: 50px; margin: 20px; width: 350px; height:50px;">
<div class="child" style="background: white; height: 100%;">
</div>
</div>
<div class="parent" style="background:gray; padding: 50px; margin: 20px; width: 350px; height:50px;">
<div class="child" style="background: white; height: 100%;">
</div>
</div>
</body>
<script>
$(document).ready(function(){
$(".parent").mouseenter(function() {
$(this).find(".child").addClass("child-show");
});
$(".parent").mouseleave(function() {
$(this).find(".child").removeClass("child-show");
});
});
</script>
</html>
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