<h1 class="padded-multiline">
  <span>How do I add padding to subsequent<br>lines of an inline text element?</span>
</h1>
.padded-multiline { 
  line-height: 1.4; 
  padding: 2px 0; 
  width: 400px;
  margin: 20px auto;
}
.padded-multiline span { 
  background: linear-gradient(to right, #c0c, red);
  color: #fff; 
  display: inline;
  padding: 0.45rem;
  
  /* Needs prefixing */
  box-decoration-break: clone;
  -webkit-box-decoration-break: clone;
}

body {
  padding: 1rem;
}

External CSS

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External JavaScript

  1. //cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js