First, we should clarify that there are two types of jihad.
Greater Jihad, which is an introspective journey to conquer your
internal demons and follow the Divine Laws more closely than
previously, is a practice to promote a person's piety. Lesser Jihad
is usually brought to life in the form of warfare between Muslims
and Non-Muslims or other Muslims, but can also be expressed in
non-violent protest or debate.
Muslims are quick to point out that the attacking of civilians
is a violation of the terms of a Lesser Jihad, but there are
serious debates in the Islamic communities worldwide as to what a
"civilian" is. A number of leading Sheikhs, including Egypt's
Qaradawi, for example, have held that since almost all Israelis are
drafted in the Israeli Defense Forces, there is no civilian
population in Israel and targeting Israeli non-combatants is NOT a
violation of the jihad requirements to avoid civilian deaths. Bin
Laden and his ilk have expanded these rulings to say that all
people in a democracy publicly vote on the government and are,
therefore, responsible for its decisions. In that way, targeting
the non-combatants in a democracy would NOT be a violation of the
jihad requirements to avoid civilian deaths. Muslims who follow
these perspectives are willing to perform violent acts against
civilians. In most cases, these civilians are Non-Muslims.
One particularly recent example of Non-Muslims killed in a
declared jihad are the Assyrian Christians and Yazidis being hunted
down by ISIL in northern Iraq. Whether ISIL is properly within the
terms of a Lesser Jihad when it performs these activities is hotly
debated in Islamic circles, but it is incorrect to say that
Non-Muslims are not being killed as a result of something that is,
at least facially, a jihad. Other examples include the Palestinian
Intifadas which primarily targeted Jewish Israeli civiians, the
Mumbai bombing which targeted primarily Hindu Indian civilians,
etc.
Note: This answer is confusing because of double-negatives and
exclusion of people groups who cannot ever be combatants, such as
Arabs married to Americans/Israelis, blind Israelis, unborn
children inside the womb of a non-Muslim, people who have no arms,
tourists.
