Read Word document line by line (Include Header and Footer)

Well the problem is that word document internally is not structured in that way, you do not have first a header lines, then a content lines, then a footer lines. Also there are few header and footer types that your document can have (first, even and default).
Nevertheless try the following:

var doc = DocumentModel.Load("Sample.docx");
 
foreach (var section in doc.Sections)
{
    HeaderFooter headerFooter;
    List<string> texts;
 
    // Read first page header's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.HeaderFirst];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
 
    // Read even pages header's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.HeaderEven];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
 
    // Read default header's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.HeaderDefault];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
 
    // Read section's text.
    texts.Add(section.Content.ToString());
 
    // Read first page footer's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.FooterFirst];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
 
    // Read even pages footer's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.FooterEven];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
 
    // Read default footer's text.
    headerFooter = section.HeadersFooters[HeaderFooterType.FooterDefault];
    if (headerFooter != null)
        texts.Add(headerFooter.Content.ToString());
}

I hope this works for you, I used the C# code with this Word component which has a really straightforward way of reading the Word documents in C#.