In Linux Libertine, the Th ligature is among the basic ones, so either you disable all of them or you get it.
A way out is to load a special mapping. Copy the tex-text.map file you find in your TeX distribution and rename it tex-text-noth.map, adding a bottom line so that it becomes
; TECkit mapping for TeX input conventions <-> Unicode characters
LHSName "TeX-text-noth"
RHSName "UNICODE"
pass(Unicode)
; ligatures from Knuth's original CMR fonts
U+002D U+002D <> U+2013 ; -- -> en dash
U+002D U+002D U+002D <> U+2014 ; --- -> em dash
U+0027 <> U+2019 ; ' -> right single quote
U+0027 U+0027 <> U+201D ; '' -> right double quote
U+0022 > U+201D ; " -> right double quote
U+0060 <> U+2018 ; ` -> left single quote
U+0060 U+0060 <> U+201C ; `` -> left double quote
U+0021 U+0060 <> U+00A1 ; !` -> inverted exclam
U+003F U+0060 <> U+00BF ; ?` -> inverted question
; additions supported in T1 encoding
U+002C U+002C <> U+201E ; ,, -> DOUBLE LOW-9 QUOTATION MARK
U+003C U+003C <> U+00AB ; << -> LEFT POINTING GUILLEMET
U+003E U+003E <> U+00BB ; >> -> RIGHT POINTING GUILLEMET
; disable Th
U+0054 U+0068 <> U+0054 U+200C U+0068
Then run
teckit_compile tex-text-noth.map
and try the following example
\documentclass{article}
\usepackage{fontspec}
\setmainfont[Mapping=tex-text-noth]{Linux Libertine O}
\begin{document}
The
\end{document}
Here's what I get:

You can move the files tex-text-noth.map and tex-text-noth.tex in your personal TeX tree (or have them in the same folder as your main file); on a Unix system you should do
mkdir -p $(kpsewhich -var-value TEXMFHOME)/fonts/misc/xetex/fontmapping/noth
cp tex-text-noth.* $(kpsewhich -var-value TEXMFHOME)/fonts/misc/xetex/fontmapping/noth/
No idea if you're using MiKTeX, sorry.
T\/hnot work? – Nov 08 '14 at 22:16search and replace Th by T\/hthe better way? ;-) – Nov 08 '14 at 22:44