Yes, there may be "soldiers" considered neutral - even if they are members of armed forces, provided that their sole duty was medical aid for the wounded ("ambulances"). The seminal document is the "initial" Geneva Convention 1864 ("Convention for the Amelioration of the Condition of the Wounded in Armies in the Field"), initiated by Henry Dunant, after the cruel battle of Solferino.
Excerpt from the 1864 convention:
Art. 1. Ambulances and military hospitals shall be recognized as neutral, and as such, protected and respected by the belligerents as long as they accommodate wounded and sick.
Neutrality shall end if the said ambulances or hospitals should be held by a military force.
Art. 2. Hospital and ambulance personnel, including the quarter-master's staff, the medical, administrative and transport services, and the chaplains, shall have the benefit of the same neutrality when on duty, and while there remain any wounded to be brought in or assisted.
Art. 3. The persons designated in the preceding Article may, even after enemy occupation, continue to discharge their functions in the hospital or ambulance with which they serve, or may withdraw to rejoin the units to which they belong.
When in these circumstances they cease from their functions, such persons shall be delivered to the enemy outposts by the occupying forces.
Art. 6. Wounded or sick combatants, to whatever nation they may belong, shall be collected and cared for. (...) Evacuation parties, and the personnel conducting them, shall be considered as being absolutely neutral.
Art. 7. A distinctive and uniform flag shall be adopted for hospitals, ambulances and evacuation parties. It should in all circumstances be accompanied by the national flag.
An armlet may also be worn by personnel enjoying neutrality but its issue shall be left to the military authorities.
Both flag and armlet shall bear a red cross on a white ground.
In 1949, four conventions ("Geneva Conventions") laid the base for international humanitarian law, including provisions regarding the treatment of the wounded as well as the status of medical units.
Here are two excerpts from the first of the 1949 conventions ("Convention (I) for the Amelioration of the Condition of the Wounded and Sick in Armed Forces in the Field"):
At all times, and particularly after an engagement, Parties to the conflict shall, without delay, take all possible measures to search for and collect the wounded and sick, to protect them against pillage and ill-treatment, to ensure their adequate care, and to search for the dead and prevent their being despoiled.
Whenever circumstances permit, an armistice or a suspension of fire shall be arranged, or local arrangements made, to permit the removal, exchange and transport of the wounded left on the battlefield.
Likewise, local arrangements may be concluded between Parties to the conflict for the removal or exchange of wounded and sick from a besieged or encircled area, and for the passage of medical and religious personnel and equipment on their way to that area.
Fixed establishments and mobile medical units of the Medical Service may in no circumstances be attacked, but shall at all times be respected and protected by the Parties to the conflict. Should they fall into the hands of the adverse Party, their personnel shall be free to pursue their duties, as long as the capturing Power has not itself ensured the necessary care of the wounded and sick found in such establishments and units.
The responsible authorities shall ensure that the said medical establishments and units are, as far as possible, situated in such a manner that attacks against military objectives cannot imperil their safety.
Regarding journalists / reporters, the situation isn't as clear as regarding ambulances. Actually, they are considered as civilians or non-combatants and protected as such (on the basis of current international humanitarian law). Attacks on civilian journalists is explicitly condemned by the UN security council (see resolution 1738, dating from 2006).