When using the following simple code with Aspose.Pdf for .NET 7.7.0, I can see Italic text and all string in H1. When using IsHtmlTagSupported, its recommended to specify the text formatting (Bold, FontSize etc) using HTML Tags.
Aspose.Pdf.Generator.Pdf pdf1 = new Aspose.Pdf.Generator.Pdf();
Aspose.Pdf.Generator.Section sec1 = pdf1.Sections.Add();
Text title = new Text("<h1>What a nice <i>italic</i> freaking title</h1>");
var info = new TextInfo();
info.FontSize = 12;
//info.IsTrueTypeFontBold = true;
title.TextInfo = info;
title.IsHtmlTagSupported = true;
sec1.Paragraphs.Add(title);
pdf1.Save("c:/pdftest/PDF_From_HTML.pdf");
Furthermore, a Text paragraph can have one or more Segment object and you can specify different formatting for each segment. In order to fulfill your requirement, you may try using the following code snippet
Aspose.Pdf.Generator.Pdf pdf1 = new Aspose.Pdf.Generator.Pdf();
Aspose.Pdf.Generator.Section sec1 = pdf1.Sections.Add();
Text title = new Text("What a nice");
var info = new TextInfo();
info.FontSize = 12;
info.IsTrueTypeFontBold = true;
title.TextInfo = info;
Segment segment2 = new Segment(" italic ");
// set the formatting of segment2 as Italic
segment2.TextInfo.IsTrueTypeFontItalic = true;
// add segment2 to segments collection of text object
title.Segments.Add(segment2);
Segment segment3 = new Segment(" freaking title ");
// add segment3 to segments collection of text object
segment3.TextInfo.IsTrueTypeFontBold = true;
title.Segments.Add(segment3);
sec1.Paragraphs.Add(title);
// save the output document
pdf1.Save("c:/pdftest/PDF_with_Three_Segments.pdf");